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Combination

If n is a pos...

Question

If n is a positive integer; then $^{n} C_{0}$ is equal to

A

n

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B

0

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C

1

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D

none of these

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Solution

The correct option is C $1$
$^{n} C_{r} = \frac{n!}{(n - r)! r!}$
$^{n} C_{0} = \frac{n!}{(n - 0)! 0!}$ $(∵ 0! = 1)$
$= \frac{n!}{n! 1}$
$= \frac{1}{1}$
$∴^{n} C_{0} = 1$

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