Question

(n+1) p5:np6=2:7 find n value​

Answer 1

Answer:

n=11

Step-by-step explanation:

(n+1) p5:np6=2:7

=> 7(n+1) p5 = 2 np6

n p r = n! /(n-r)!

hence

7((n+1)!/(n+1-5)! ) = 2n!/(n-6)!

=> 7(n+1)n!/(n-4)! = 2n!/(n-6)!

cancelling n! from both sides

=> 7(n+1)/(n-4)! = 2/(n-6)!

=> 7(n+1) = 2(n-4)!/(n-6)!

=> 7(n+1) = 2(n-4)(n-5)(n-6)!/(n-6)!

=> 7n + 7 = 2 (n-4)(n-5)

$7n + 7 = 2( {n}^{2} - 9n + 20) \\ 2 {n}^{2} - 25n + 33 = 0 \\ 2 {n}^{2} - 22n - 3n + 33 = 0$

2n(n-11)-3(n-11)= 0

(2n-3)(n-11)= 0

n = 11

Answer 2

Step-by-step explanation:

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