Question

if nPr=2520 and nCr=21 find r​

Answer 1

GIVEN :

If  $^nP_r=2520$ and $^nC_r=21$ 

TO FIND :

The value of r in the given values.

SOLUTION :

Given that the values are  $^nP_r=2520$ and $^nC_r=21$

The formulae are given by :

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

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

Since $^nP_r=2520$ and $^nC_r=21$ we have that  

$^nP_r=\frac{n!}{(n-r)!}=2520\hfill (1)$

and $^nC_r=\frac{n!}{r! (n-r)!}=21\hfill (2)$

Rearranging  but   Also, so they are equivalent,  

The $(n-r)!$ terms cancel on both sides, leaving $r! = \frac{2520}{21}$

$\frac{2520}{r!} = 21$

$r!= \frac{2520}{21}$

$r!=120$

$r!=5!$

⇒ r = 5

∴ the value of r is 5