Question

for which values of r nCr = nPr​

Answer 1

Given :

n C r = n P r​

To Find :

The value of r

Solution :

∵  n C r = n P r​

So,   $\dfrac{\angle n}{\angle (n-r)}$ =  $\dfrac{\angle n}{\angle r\angle (n-r)}$

Or,  $\angle r$  = 1

So,  ! r = 0 , 1

Now,

Let n = 5 , r = 1

 $\dfrac{\angle 5}{\angle (5-1)}$ =  $\dfrac{\angle 5}{\angle 1\angle (5-1)}$

               = $\dfrac{\angle 5}{\angle 1\angle (4)}$

               = $\dfrac{5!4}{!4}$

               = 5

Again

Let n = 5 , r = 0

 $\dfrac{\angle 5}{\angle (5-0)}$ =  $\dfrac{\angle 5}{\angle 0\angle (5-0)}$

                = $\dfrac{!5}{!0}$

                = 1

   So, here Two case raises that the value of r = 1 , 0  , but the value of r should be 1 for the condition to be true

Hence,  The value of r should be 1 for the condition to be true . Answer