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nCr Definitions and Properties

The value of ...

Question

The value of ${}^{15}{C_{8} + {}^{15}{C_{9} - {}^{15}{C_{6} - {}^{15}{C_{7}}}}}$ is

A

$- 1$

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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 B
$0$

The explanation for the correct answer.
Given: ${}^{15}{C_{8} + {}^{15}{C_{9} - {}^{15}{C_{6} - {}^{15}{C_{7}}}}}$
We know that ${}^{n}C_{r} = {}^{n}{C_{n - r}}$
${}^{15}{C_{7} + {}^{15}{C_{6} - {}^{15}{C_{6}} - {}^{15}{C_{7}}}} = 0$
Hence $o ption (B)$ is the correct answer.

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