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

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Solution

Finding the sum of series
It is given that $(^{15} C_{8} +^{15} C_{9}) - (^{15} C_{6} +^{15} C_{7})$
Using $^{n} C_{r} +^{n} C_{r - 1} =^{n + 1} C_{r}$
$=^{16} C_{9} -^{16} C_{7}$
$=^{16} C_{9} -^{16} C_{16 - 7}$
$=^{16} C_{9} -^{16} C_{9} = 0$
Hence, the value of
$^{15} C_{8} +^{15} C_{9} -^{15} C_{6} -^{15} C_{7}$ is 0.

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