Question

Find x, if $\rm ^{n}C_{r} = x.\ \rm ^{n}P_{r}$

Answer 1

Answer:

1/r!

Step-by-step explanation:

Hi,

Given that ⁿCr = x.ⁿPr

But we know from the identity that,

ⁿCr  = n!/(n-r)!r! and

ⁿPr = n!/(n-r)!

Thus, we are given that

n!/(n-r)!r!  = x.n!/(n-r)!

n! and (n-r)! gets cancelled out and we are left with

⇒ x = 1/r!

Hence, the value of x is 1/r!

Hope, it helps !