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nCr Definitions and Properties

IF nCr=nPr t...

Question

IF $^{n} C_{r} =^{n} P_{r}$ then r can be____

A

0

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B

1

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C

3

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D

Either(1) or (2)

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Solution

The correct option is D Either(1) or (2)
Given,
$^{n} C_{r} =^{n} P_{r}$
$=> \frac{n!}{(r!) (n - r)!} = \frac{n!}{(n - r)!}$
$=> r! = 1$
$=> r = 0$ or $1$ as $0! = 1; 1! = 1$

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