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Mathematics Question on Combinations

The value of  16C9+ 16C10− 16C6− 16C7\,^{16}C_9 + \,^{16}C_{10} -\,^{16}C_6 -\,^{16}C_7 is

A

0

B

1

C

17C10^{17}C_{10}

D

17C3^{17}C_3

Answer

0

Explanation

Solution

16C9+16C10−16C6−16C7{ }^{16} C _{9}+{ }^{16} C _{10^{-}}{ }^{16} C _{6^{-}}{ }^{16} C _{7}
=16C9+16C10−16C10−16C9=0={ }^{16} C _{9}+{ }^{16} C _{10^{-}}{ }^{16} C _{10^{-}}{ }^{16} C _{9}=0
(∵nCr=nC(n−r))\left(\because{ }^{ n } C _{ r }={ }^{ n } C _{( n - r )}\right)