The value of C 9 16 + C 10 16 - C 6 16 - C 7 16 is

Question

The value of ${}^{16}C_{9} + {}^{16}C_{10} - {}^{16}C_{6} - {}^{16}C_{7}$ is

Smart Achievers · Accepted Answer

(4)

We have, ${}^{16}C_{9} + {}^{16}C_{10} - {}^{16}C_{6} - {}^{16}C_{7}$

$= {}^{17}C_{10} - {}^{17}C_{7}$ $(∵ {}^{n}C_{r} + {}^{n}C_{r - 1} = {}^{n + 1}C_{r})$

$= {}^{17}C_{10} - {}^{17}C_{10}$ $(∵ {}^{n}C_{r} = {}^{n}C_{n - r})$

$= 0$

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