CMAT 2016 Solved Question Paper

Question : 23 of 100

Marks: +1, -0

If six times the number of permutations of n things 4 together is equal to one-seventh of the number of permutations of n things 6 together, then n is equal to

Validate

Solution:

^nP_4

1/7

⋅

^nP_6

⇒

{6⋅n!}/(n-4)! = 1/7 {n! /{(n-6)!

⇒

6/(n-4)! = 1/{7(n-6)!}

⇒

6/{(n-4)(n-5)(n-6)! } = 1/{7(n-6)!}

⇒ 42 = (n - 4)(n - 5)
⇒ 42 =

n^2

- 9n + 20
⇒

n^2

- 9n - 22 = 0
∴ n=

{9 ± √{9^2-4 ×(-22)}}/2

{9±√{81+ 88}}/2

{9± √169}/2

{9±13}/2

Hence, n = 11

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