${}^{15}C_{8} + {}^{15}C_{9} - {}^{15}C_{6} - {}^{15}C_{7} = ?$

$1$

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$2$

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$0$

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$N o n e o f t h e s e$

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Solution

The correct option is C
$0$

Explanation for the correct option:
Let $S = {}^{15}C_{8} + {}^{15}C_{9} - {}^{15}C_{6} - {}^{15}C_{7} = ?$
As we know, ${}^{n}C_{r} = {}^{n}C_{n - r}$
Apply the formula on the first $2$ terms of the given series, we get
$\Rightarrow S = {}^{15}C_{15 - 8} + {}^{15}C_{15 - 9} - {}^{15}C_{6} - {}^{15}C_{7}$
$\Rightarrow S = {}^{15}C_{7} + {}^{15}C_{6} - {}^{15}C_{6} - {}^{15}C_{7}$
$\Rightarrow S = 0$
Hence, Option C is correct.

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C815+C915-C615-C715=?

The correct option is C 0Explanation for the correct option:Let S=C815+C915-C615-C715=?As we know, Crn=Cn-rnApply the formula on the first 2 terms of the given series, we get⇒S=C15-815+C15-915-C615-C715⇒S=C715+C615-C615-C715⇒S=0Hence, Option C is correct.

${}^{15}C_{8} + {}^{15}C_{9} - {}^{15}C_{6} - {}^{15}C_{7} = ?$