Question

(17 -n)!/(14-n)!=5!
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Answer 1

Answer:

11

Step-by-step explanation:

It implies

( 15-n)(16-n)(17-n)=5!=1*2*3*4*5=4*5*6

So 15-n=4

16-n=5

17-n=6

As 15-n is smaller than other 2 and 17-n is the largest.

Hence, n=15-4=11

Answer 2

The value of n is 11

Step-by-step explanation:

Given :  $\frac{(17-n)!}{(14-n)!}=5!$

Solution:

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

$\frac{(17-n)(16-n)(15-n)(14-n)!}{(14-n)!}=5!\\(17-n)(16-n)(15-n)=5 \times 4 \times 3 \times 2 \times 1\\(17-n) \times (16-n) \times (15-n)=5 \times 4 \times 3 \times 2 \times 1\\-n^3+48n^2-769n+4080=120\\n=11$

Hence The value of n is 11

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(17 -n)!/(14-n)!=5!