Question

npr =720 and ncr =120 find r

Answer 1

Answer:

The value of r is 3.

Step-by-step explanation:

Given : $^nP_r=720$ and $^nC_r=120$

To find : The value of r ?

Solution :

We know that,

$^nP_r=\frac{n!}{(n-r)!}$

So, $\frac{n!}{(n-r)!}=720$  .....(1)

$^nC_r=\frac{n!}{r!(n-r)!}$

So, $\frac{n!}{r!(n-r)!}=120$  .....(2)

Divide (1) and (2),

i.e. $\frac{^nP_r}{^nC_r}=\frac{720}{120}$

$\frac{\frac{n!}{(n-r)!}}{\frac{n!}{r!(n-r)!}}=\frac{720}{120}$

$r!=6$

$r!=3\times 2\times 1$

$r!=3!$

Therefore, The value of r is 3.