Question

Find n, if:
(17-n)!/(14-n)!=5!​

Answer 1

Answer:

n = 11

Step-by-step explanation:

Given : $\frac{(17-n)!}{(14-n)!}=5!$

To Find : n

Solution :

$\frac{(17-n)!}{(14-n)!}=5!$

$\frac{(17-n) \times (17-n-1) \times (17-n-2) \times (17-n-3)!}{(14-n)!}=5!$

$\frac{(17-n) \times (16-n) \times (15-n) \times (14-n)!}{(14-n)!}=5!$

$(17-n) \times (16-n) \times (15-n)=5 \times 4 \times 3 \times 2 \times 1$

$-n^3+48n^2-769n+4080=120$

$n=11$

Hence the value of n is 11