P(7,r)= 840, then r=?
1. P(7,r)= 840, then r=?
[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]
P(7,r) = 840
P(7,r) = n! / (n-r)!840 = 7! / (7-r)!(7-r)! = 7! / 840(7-r)! = 5040 / 840(7-r)! = 6notice that 6 can be written as 3!
(7-r)! = 3!cancel the factorial sign
7-r = 37-3 = r 4 = r[tex] \\ [/tex]
[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
The value of r is 42. P(7,r)=840 what is r? (permutation)
P(7, 4) = 840
7 x 5 x 4 x 3 = 840
3. What is the answer of p(7,r)=840
Answer: r =4
Explanation: p(7,r)= 840
P(7,r) = [tex] \frac{n!}{n-r}! where P(p,r)[/tex]
840= 7!/(7-4)!
4. If P(n,4) =840, what is n?A. 8B. 7C. 6D. 5
Answer:
A
Step-by-step explanation:
sana makalutong pa brainliest din
5. 1. P (9. 3) = x2. P (n. 2) = 423. P (n. 4) =8404. P (11.r) = 1105. P (9. r) = 72
Answer:
Maginstall ka po ng Gauthmath sobrang ganda po ng app na yan kase tamang sagot talaga binibigay nila mga tutor po ang sumasagot sa mga tanong sa math itype nyo lang po itong Invitation Code X3LKRX para magamit nyo po yung apps sana makatulong po yung apps yan po kase gamit kong apps
Step-by-step explanation:
pa follow po thanks
6. how can i determine what is the value of n in P(7,r)=840 in permutation ?
Solve for r
7!/(7-r)! = 840
7!/840=(7-R)!
7*6*5*4*3*2*1/840=(7-R)!
3*2*1=(7-R)!=3!
7-R=3
R=7-3=4
7. Directions: Evaluate each Permutation. Write the answers in a separate paper1. P (9, 3) = x2. P (n. 2) = 423. P (n. 4) =8404. P (11.r) = 1105. P (9.7) = 72
Explanation:
I'm not sure po kung Tama bayan.#keepsafepo
8. Please answerPermutations 1. P(n,3) = 60 2.P(7,r) = 840
Permutation of n taken r has the formula,
[tex]P(n,r)= \frac{n!}{(n-r)!} [/tex]
1. P(n,3)=60
[tex] \frac{n!}{(n-3)!} =60[/tex]
[tex] \frac{n(n-1)(n-2)(n-3)!}{(n-3)!} =60[/tex] -Factor n! up to (n-3)!
Since (n-3)! divided by itself is equal to 1, Then,
[tex]n(n-1)(n-2)=60[/tex]
The left side of the equation has 3 consecutive descending factors, do the same with 60,
[tex]n(n-1)(n-2)=(5)(4)(3)[/tex]
Both sides have the same order, therefore, n = 5
2. P(7,r)=840
[tex] \frac{7!}{(7-r)!} =840[/tex]
[tex] \frac{5040}{(7-r)!} =840[/tex]
[tex] \frac{5040}{840} =(7-r)![/tex]
[tex]6=(7-r)![/tex]
Note that there is only one factorial that would result to 6, that is, 3!.
So,
7-r=3
r=4
9. Activity 2 Supply the correct answer in each number. 1. P (7,0) = 840, then r= 2. Pln, 3) = 60, then n= 3. P ( 10,5) = 4. P (8,0) = 6, 720, then r= 5. P (8,3 ) = Activity 3 To the next levell
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• Take responsibility for your actions Volunteer to be active in your community.
Be honest and trustworthy.
Follow rules and laws.
Respect the rights of others.
Be informed about the world around you
Respect the property of others.
Be compassionate.
• Take responsibility for your actions Volunteer to be active in your community.
Be honest and trustworthy.
Follow rules and laws.
Respect the rights of others.
Be informed about the world around you
Respect the property of others.
Be compassionate.
• Take responsibility for your actions Volunteer to be active in your community.
Be honest and trustworthy.
Follow rules and laws.
Respect the rights of others.
Be informed about the world around you
Respect the property of others.
Be compassionate.
• Take responsibility for your actions Volunteer to be active in your community.
Be honest and trustworthy.
Follow rules and laws.
Respect the rights of others.
Be informed about the world around you
Respect the property of others.
Be compassionate.
• Take responsibility for your actions Volunteer to be active in your community.
Be honest and trustworthy.
Follow rules and laws.
Respect the rights of others.
Be informed about the world around you
Respect the property of others.
Be compassionate.
• Take responsibility for your actions
10. P(7,r)=840 what is rdand its formula
[tex]P(n,r)= \frac{n!}{(n-r)!} \\ \\ P(7,r)=840 \\ \\ 840= \frac{7!}{(7-r)!} \\ \\ 840(7-r)!=7! \\ \\ (7-r)!= \frac{5040}{840} \\ \\ (7-r)!=6[/tex]
And we know that [tex]3!=6[/tex], therefore,
[tex]7-r=3 \\ \\ r=4[/tex]
11. Activity 2: KEEP PRACTICINGIDirection: Solve for the unknown in each item,1. P(5,5) =2. P(7, r) = 8403. P(n, 3) = 504
Answer:
P=120
Step-by-step explanation:
P(5,5)=?
P(n,r)=n!/(n-r)!P(5,5)=5!/(5-5)!P(5,5)=5!/0!P(5,5)=120/1P(5,5)=12012. Activity 4: LET'S PRACTICE!Direction: Evaluate each expression.1. 4P22. P(5,5)3. P(7, r) = 8404. -4 + 7P45. 5 . 6Ps
Answer:
1.P6
2.5 (25)
3.P (7r)
4.7P
5.30ps.
13. If P(n,4) =840, what is n? A. 8 B. 7 C. 6 D. 5
Answer:
letter d po
Step-by-step explanation:
brainliest me plss
14. activity 5: warm that mind up! solve for the unknown in each item, and then answer the questions that follow with solution 1.P(6,6)= 2.P(7,r)=840 3.P(n,3)=60 4.P(n,3)=504 5.P(10,5)= 6.P(8,r)=6720 7.P(8,3)= 8.P(n,4)=3024 9.P(12,r)=1320 10.P(13,r)=156
Answer:
1. 720; 5. 30,240; 7. 336
Step-by-step explanation:
[tex]P(n,r) = \frac{n!}{(n-r)!}[/tex]
1. [tex]P(6, 6) = \frac{6!}{(6-6)!}[/tex]
[tex]= \frac{6!}{0!}[/tex] (Take note that 0! = 1, not zero)
[tex]= \frac{6!}{1}[/tex]
= 6 x 5 x 4 x 3 x 2 x 1
= 720
5. [tex]P(10,5) = \frac{10!}{(10-5)!}[/tex]
[tex]= \frac{10!}{5!}[/tex]
= 10 x 9 x 8 x 7 x 6
= 30,240
7. [tex]P (8, 3) = \frac{8!}{(8-3)!}[/tex]
[tex]= \frac{8!}{5!}[/tex]
= 8 x 7 x 6
= 336
If you want to try answering more questions related to permutations and combinations, click on any of these links below:
brainly.ph/question/1308910
brainly.ph/question/1459992
brainly.ph/question/2101331
15. Learning Task 3: Solve for the unknown in each item, and then answer the questions that follow. 1. P(6, 6) = ___ 2. P(7, r) = 840 3. P(8, 3) = ___ 4. P(n, 3) = 504 5. P(10, 5) = ___plss pa answer po :(
✏️PERMUTATIONS
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex] \underline{\mathbb{DIRECTIONS:}} [/tex]
Solve for the unknown in each item, and then answer that questions that follow.[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex] \underline{\mathbb{ANSWER:}} [/tex]
[tex] \qquad\Large\rm» \:\: 1. \: \green{P(6,6) = 720} [/tex]
[tex] \qquad\Large\rm» \:\: 2. \: \green{r = 3} [/tex]
[tex] \qquad\Large\rm» \:\: 3. \: \green{P(8,3) = 336} [/tex]
[tex] \qquad\Large\rm» \:\: 4. \: \green{n = 9} [/tex]
[tex] \qquad\Large\rm» \:\: 5. \: \green{P(10,5) = 30\text,240} [/tex]
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex] \underline{\mathbb{SOLUTIONS:}} [/tex]
» Using the Permutation Formula to find the values.
[tex]\begin{aligned} & \bold{\color{lightblue}Formula:} \\ & \boxed{\: \rm _nP_r = \frac{n!}{(n-r)!} \:} \end{aligned} [/tex]
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#1. P(6,6) [tex]\begin{aligned} \rm P(6,6) = \frac{6!}{(6 - 6)!} \end{aligned} [/tex][tex]\begin{aligned} \rm P(6,6) = \frac{ \: 6! \: }{0!} \end{aligned} [/tex][tex]\rm P(6,6) = 6! [/tex][tex]\rm P(6,6) = 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2[/tex][tex]\rm P(6,6) = 720[/tex][tex] \therefore [/tex] The number of permutations is 720.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#2. P(7, r) = 840[tex]\begin{aligned} \rm P(7,r) = \frac{7!}{(6 - r)!} \end{aligned} [/tex][tex]\begin{aligned} \rm 840 = \frac{7!}{(6 - r)!} \end{aligned}[/tex]» Exchange 840 and (6 - r)!
[tex]\begin{aligned} \rm (6 - r)! = \frac{7!}{840} \end{aligned}[/tex][tex]\begin{aligned} \rm (6 - r)! = \frac{ \cancel{840} \cdot 3!}{ \cancel{840}} \end{aligned}[/tex][tex]\rm (6 - r)! = 3![/tex]» Removed (!) on both sides.
[tex]\rm 6 - r = 3[/tex][tex]\rm r = 6 - 3[/tex][tex]\rm r = 3[/tex][tex] \therefore [/tex] The value of r is 3.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#3. P(8, 3)[tex]\begin{aligned} \rm P(8,3) = \frac{8!}{(8 - 3)!} \end{aligned}[/tex][tex]\begin{aligned} \rm P(8,3) = \frac{ \: 8! \: }{5!} \end{aligned}[/tex][tex]\begin{aligned} \rm P(8,3) = \frac{ \: 8 \cdot 7 \cdot 6 \cdot \cancel{5!} \: }{ \cancel{5!}} \end{aligned}[/tex][tex]\rm P(8,3) = 8 \cdot 7 \cdot 6[/tex][tex]\rm P(8,3) = 336[/tex][tex] \therefore [/tex] The number of permutations is 336.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#4. P(n, 3) = 504[tex]\begin{aligned} \rm P(n,3) = \frac{n!}{(n - 3)!} \end{aligned}[/tex][tex]\begin{aligned} \rm 504 = \frac{n!}{(n - 3)!} \end{aligned}[/tex]» Simplify by canceling.
[tex]\begin{aligned} \rm 504 = \frac{n(n - 1)(n - 2) \cancel{(n - 3!)}}{ \cancel{(n - 3)!}} \end{aligned}[/tex][tex]\rm 504 = n(n - 1)(n - 2)[/tex]» Expand to get the product.
[tex]\rm 504 = {n}^{3} - 3n^{2} + 2n [/tex][tex]\rm {n}^{3} - 3n^{2} + 2n - 504 = 0[/tex]» Factor out then apply the Zero Product Property.
[tex]\rm (n - 9)( {n}^{2} + 6n + 56) = 0[/tex][tex]\rm n - 9 = 0 \quad; \quad {n}^{2} + 6n + 56 = 0[/tex][tex]\rm n = 9 \quad; \quad “No \ real \ solutions” [/tex][tex] \therefore [/tex] The value of n is 9.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#5. P(10, 5)[tex]\begin{aligned} \rm P(10,5) = \frac{10!}{(10 - 5)!} \end{aligned}[/tex][tex]\begin{aligned} \rm P(10,5) = \frac{ \: 10! \: }{5!} \end{aligned}[/tex][tex]\begin{aligned} \rm P(10,5) = \frac{ \: 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot \cancel{5!} \: }{ \cancel{5!}} \end{aligned}[/tex][tex]\rm P(10,5) = 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 [/tex][tex]\rm P(10,5) = 30\text,240 [/tex][tex] \therefore [/tex] The number of permutations is 30,240.
[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#CarryOnLearning
✏️ PERMUTATIONS[tex] \color{darkblue}••••••••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
Learning Task 3: Solve for the unknown in each item, and then answer the questions that follow.
1. P(6, 6) = ___ 2. P(7, r) = 840 3. P(8, 3) = ___ 4. P(n, 3) = 504 5. P(10, 5) = ___[tex] \color{darkblue}••••••••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
THE ANSWER ☕
1). P(6, 6) = 720
2). P(7, r) = 840 = r = 3
3). P(8, 3) = 336
4). P(n, 3) = 504 = n = 9
5). P(10, 5) = 30,240
[tex] \color{darkblue}••••••••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]
16. P(7,r)=840,then r=?______. p(n,3)=60,then n=?______. p(10,5=?_______. p(8,r)=6.720,then r=? p(8,3)=?_______
Answer:
combination or permutation?
Step-by-step explanation:
sabihin mo lang kung ano yan aansweran konon after
17. Supply the conect answer in each number 1. P 17.1] = 840, then r= 2. Pin. 3) = 60. then n= 3. P(10.5)= 4. P 18.1) = 6,720 then = 5. P (8,3 ) =
Answer:
sorry po diko po alama
Step-by-step explanation:
[tex]\blue{ \rule{0pt}{99999pt}}[/tex]
hello po sorry po kung may nag answer ng Hindi Ang tunay na answer
18. Solve for the unknown in each item, and then answer the questions that follow. 2. P(7, r) = 840
p (7,4) = 840
7 x 6 x 5 x 4 = 840
19. P (n,4)=840= find the objects
Answer:
[tex]P(n,4) = 840[/tex]
[tex]P(n,r) = \frac{n!}{(n - r)!} [/tex]
[tex]840 = \frac{n!}{(n - 4)!} [/tex]
[tex]840 = \frac{(n)(n - 1)(n - 2)(n - 3)(n - 4)!}{(n - 4)!} [/tex]
cancel (n - 4)!
[tex]840 = (n)(n - 1)(n - 2)(n - 3)[/tex]
[tex]840 = (n)(n - 1)( {n}^{2} - 5n + 6)[/tex]
[tex]840 = (n)( {n}^{3} - 5 {n}^{2} + 6n - {n}^{2} + 5n - 6)[/tex]
[tex]840 = (n)( {n}^{3} - 6 {n}^{2} + 11n - 6)[/tex]
[tex]840 = {n}^{4} - 6 {n}^{3} + 11 {n}^{2} - 6n[/tex]
[tex] {n}^{4} - 6 {n}^{3} + 11 {n}^{2} - 6n - 840 = 0[/tex]
the roots are:
[tex]n = - 4,7, \frac{3 + i \sqrt{111} }{2} , \frac{3 - i \sqrt{111} }{2} [/tex]
take the positive whole number.
n = 7
20. 1.P (n, 2} = 30 *2 pointsA. r= 6B. n=6C. n= 7D. r= 72.P (7, r) = 840 *2 pointsr= 4n= 4r=5n= 53.C (n,10) = 3C (n, 9) *2 pointsA. n= 37B. n= 38C. n= 39D. n= 404.C (13, r) = 286 *2 pointsA. r=3B. r=4C. r=5D. r=65.C (n, r) = 4 and P (n, r) = 24 *2 pointsA. n=4, r=3B. n=5, r=3C. n=4, r=4D. n=6, r=3
Answer:
1.A
2.C
3.D
4.B
5.C
Step-by-step explanation:
pls correct me if I wrong
21. A. Evaluate the following: 1. P(8,2) 2. ¹¹PS53. P(7,r) = 840 4. P(5,5) 5. P{n, 4) = 1680
Answer:
1.76.2
2.27
3.847.0⁰
4same answer in no.1
5.its not exact answer
22. Activity 1: Warm That Mind Up! Directions: Determine the unknown in ec follow. Use a separate sheet of paper. 2 P(7.r) = 840 1. P(6, 6)= 3 P (n, 3) = 60 4. P (8, 3) = 5. P (n, 4) 3024 opg
[tex]\large\purple{{{\sf{Hi!}}}}[/tex]
[tex]\large\tt\purple{⊱─━━━━━━━⊱༺●༺⊰━━━━━━━─⊰}[/tex]
2. P(7, r) = 840
[tex]\large\sf\purple{r = 4}[/tex]
1. P(6, 6) =
[tex]\large\sf\purple{720}[/tex]
3. P(n, 3) = 60
[tex]\large\sf\purple{n = 5}[/tex]
4. P(8, 3) =
[tex]\large\sf\purple{336}[/tex]
5. P(n, 4) = 3024
[tex]\large\sf\purple{n = 9}[/tex]
[tex]\large\tt\purple{⊱─━━━━━━━⊱༺●༺⊰━━━━━━━─⊰}[/tex]
[tex]\large\tt{◡̈CarryOnLearning}[/tex]
23. Supply the correct answer in each number. 1. P (7,0) = 840, then r = 2. Pin, 3) = 60, then n= 3. P ( 10,5)= 4. P (8,0) = 6, 720, then r= 5. P (8,3 ) =
Step-by-step explanation:
like rn sn Maka tolong
24. 9. If 7.1) =840,what is r?.
Answer:
P ( n , r ) = n / ( n = r ) P ( 7 , r ) =840 , 840 7 / ( 7 = r ) 840 ( 7 - r ) = 7
Step-by-step explanation:
( 7 - r ) = 5040 / 840 , ( 7 - r ) = 6 7 - r = 3 , r = 4 Yan lang alam
25. 1.P(6,6)=_____ 2.P(7,r)=840 3.P(n,3)=60 4.P(n,3)=504 5.P(10,5)=_____ 6.P(8,r)=6720 7.P(8,3)=_____ 8.P(n,4)=3024 9.P(12,r)=1320 10.P(13,r)=156
1. 720
2. 4
3. 5
4. 9
5. 30,240
6. 5
7. 336
8. 9
9. 3
10. 2
26. Learning Task 2Solve for the unknown in each item1. P(6.6)2. P(7.r) - 8403. P(n,3) 5044. P(10,5)5. P(13.2) -
Answer:
1. 720
2. (7.4)
3. (9.3)
4. 30,240
5. 156
Step-by-step explanation:
1. 6×5×4×3×2×1=7202. 7×6×5×4=8403. 9×8×7=5044. 10×9×8×7=30,2405. 13×12=15627. Learning Task 3:Solve for the unknown in each item, and then answer the questions that follow.1. P(6, 6) = ___ 2. P(7, r) = 840 3. P(8, 3) = ___ 4. P(n, 3) = 504 5. P(10, 5) = ___plss pa answer po :(
1. P(6,6) = 6! = 6x5x4x3x2x1 = 1203. P(8.3) = 8x7x6 = 3365. P(10,5) = 10! = 10x9x8x7x6 = 30240#CarryOnLearing#FollowForMoreSALAMATH
28. P(7,r)=840? what is the formula about this?
to get the value of "r" let r= 4
P(7,4)=7.6.5.4
=840
29. P(6,6)= P(7,r)=840 P(n,3)=60 P(10,5)=
Answer:
720
3
5
30,240
Step-by-step explanation:
P(6,6)=(6-6)!=0!
6x5x4x3x2x1=720
P(7,r)=840=(7-3)!
7x6x5x4=840
P(n,3)=60=(5-3)!=2!
5x4x3=60
P(10,5)=(10-5)=5! 10x9x8x7x6=30,240
30. ACTIVITY 2: KEEP PRACTICING!Direction: Solve for the unknown in each item.1. P(5,5)2. P(7, r) = 8403. P(n, 3) = 5044. Pn.n-1) = 65. P(16,4) = 208. Pân, 2)
[tex] \large\underline \mathcal{{QUESTION:}}[/tex]
Direction: Solve for the unknown in each item.
1. P(5,5)
2. P(7, r) = 840
3. P(n, 3) = 504
4. P(n,n-1) = 6
5. P(16,4) = 208P(n, 2)
[tex]\\[/tex]
[tex] \large\underline \mathcal{{SOLUTION:}}[/tex]
1. [tex]\rm{P(n,r)= \frac{n!}{(n-r)!}}[/tex]
[tex]\sf{P(5,5)= \frac{5!}{(5-5)!}}[/tex]
[tex]\sf{P(5,5)= \frac{5!}{(0)!}}[/tex]
[tex]\sf{P(5,5)= \frac{5×4×3×2×1}{1}}[/tex]
[tex]\sf{P(5,5)= 5×4×3×2×1}[/tex]
[tex]\boxed{\rm{P(5,5)= 120}}[/tex]
[tex]\\[/tex]
2. [tex]\rm{P(n,r)= \frac{n!}{(n-r)!}}[/tex]
[tex]\sf{P(7,r)= \frac{7!}{(7-r)!}}[/tex]
[tex]\sf{840= \frac{7!}{(7-r)!}}[/tex]
[tex]\sf{840(7-r)!= 7!}[/tex]
[tex]\sf{840(7-r)!= 7×6×5×4×3×2×1}[/tex]
[tex]\sf{840(7-r)!=5040}[/tex]
[tex]\sf{(7-r)!=\frac{5040}{8040}}[/tex]
[tex]\sf{(7-r)!=6 }[/tex]
[tex]\textsf{express 6 as 3!}[/tex]
[tex]\sf{(7-r)! = 3!}[/tex]
[tex]\textsf{cancel out factorial sign}[/tex]
[tex]\sf{7-r=3}[/tex]
[tex]\sf{7-3=r}[/tex]
[tex]\boxed{\rm{4=r }}[/tex]
[tex]\\[/tex]
3. [tex]\rm{P(n,r)= \frac{n!}{(n-r)!}}[/tex]
[tex]\sf{P(n,3)=\frac{n!}{(n-3)!}}[/tex]
[tex]\sf{504=\frac{n!}{(n-3)!}}[/tex]
[tex]\textsf{expand n!}[/tex]
[tex]\sf{504=\frac{n(n-1)(n-2)(n-3)!}{(n-3)!}}[/tex]
[tex]\sf{504=\frac{n(n-1)(n-2)\cancel{(n-3)!}}{\cancel{(n-3)!}}}[/tex]
[tex]\sf{504=n(n-1)(n-2)}[/tex]
[tex]\sf{504=n³-3n²+2n}[/tex]
[tex]\sf{0=n³-3n²+2n-504}[/tex]
[tex]\sf{0=(n-9)(n²+6n+56)}[/tex]
[tex]\textsf{\small{Neglecting the other root , we will get the positive}}[/tex][tex]\textsf{\small{value}}[/tex]
[tex]\sf{0=n-9}[/tex]
[tex]\boxed{\sf{n=9}}[/tex]
[tex]\\[/tex]
4. [tex]\rm{P(n,r)= \frac{n!}{(n-r)!}}[/tex]
[tex]\sf{P(n,n-1)=\frac{n!}{(n-(n-1))!}}[/tex]
[tex]\sf{6=\frac{n!}{(n-n+1)!}}[/tex]
[tex]\sf{6=\frac{n!}{(1)!}}[/tex]
[tex]\sf{6=n!}[/tex]
[tex]\textsf{Remember that 3! = 6}[/tex]
[tex]\sf{6=3! \:,\boxed{\sf{n=3}}}[/tex]
[tex]\\[/tex]
5. [tex]\sf{P(16,4)=208P(n,2)}[/tex]
[tex]\sf{\frac{16!}{(16-4)!}=208(\frac{n!}{(n-2)!})}[/tex]
[tex]\sf{\frac{16!}{12!}=208(\frac{n(n-1)(n-2)!}{(n-2)!})}[/tex]
[tex]\sf{\frac{16×15×14×13×12!}{12!}=208(\frac{n(n-1)\cancel{(n-2)!}}{\cancel{(n-2)!}})}[/tex]
[tex]\sf{16×15×14×13=208[n(n-1)]}[/tex]
[tex]\sf{43,680=208(n²-n)}[/tex]
[tex]\sf{\frac{43,680}{208}=(n²-n)}[/tex]
[tex]\sf{210=(n²-n)}[/tex]
[tex]\sf{0=n²-n-210}[/tex]
[tex]\sf{0=(n-15)(n+14)}[/tex]
[tex]\textsf{\small{Neglecting the other root , we will get the positive}}[/tex][tex]\textsf{\small{value}}[/tex]
[tex]\sf{0=n-15}[/tex]
[tex]\boxed{\sf{15=n}}[/tex]
[tex]\\[/tex]
[tex] \large\underline \mathcal{{ANSWER:}}[/tex]
120r = 4n = 9n = 3n = 15