Question

np5 = 336. Find in n ​

Answer 1

ANSWER:

Given:

np5 = 336.

To find:

Find the value of np

Solution:

np + 5 = 336

I take, n value is 300 and p value is 31

so, n = 300 and p = 31

n = 300

p = 31

300 + 31 + 5 = 336

Therefore:-

n = 300

p = 31

Answer 2

np5 = 336. The value of n would be 8

Given:

np5 = 336.

To find:

The value of n.

Solution:

The product of an integer along with all the other integers less than that number is till it reaches 1 is known as the factorial of a number.

Generally,  $np_{r}$ = $\frac{n!}{(n-r)!}$

similarly, $nc_{r}$ = $\frac{n!}{(n-r)! r!}$

From the above formulae $np_{r}$ is the factorial of n divided by the factorial of n-r.

Here, r = 5

and the value = 336

(n-5)! = (n-5)(n-4)(n-3)(n-2)(n-1)(n!)

so, 336 = $\frac{n!}{(n-5)!}$

     336 = $\frac{n!}{(n-5)(n-4)(n-3)(n-2)(n-1)(n!)}$

     336 = $\frac{1}{(n-5)(n-4)(n-3)(n-2)(n-1)}$

after solving, we get

n = 8.

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