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Question: If <sup>n+5</sup>P<sub>n+1</sub>= \(\frac{11(n - 1)}{2}\). <sup>n+3</sup>P<sub>n</sub>, then the val...

If n+5Pn+1= 11(n−1)2\frac{11(n - 1)}{2}. n+3Pn, then the value of n is –

A

2 or 6

B

2 or 11

C

7 or 11

D

6 or 7

Answer

6 or 7

Explanation

Solution

(n+5)!(n+5−n−1)!\frac{(n + 5)!}{(n + 5 - n - 1)!}= 11(n−1)2\frac{11(n - 1)}{2} × (n+3)!(n+3−n)!\frac{(n + 3)!}{(n + 3 - n)!}

(n+5)(n+4)2\frac{(n + 5)(n + 4)}{2}= 11 (n – 1)

n2 + 9n + 20 = 22n – 22 Ž n = 6, 7