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  4. The value of 16C9 + 16C10 - 16C6 - 16C7 is

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Q. The value of $\,{}^{16}C_9 + \,{}^{16}C_{10} -\,{}^{16}C_6 -\,{}^{16}C_7$ is

KCETKCET 2020

Solution:

${ }^{16} C _{9}+{ }^{16} C _{10^{-}}{ }^{16} C _{6^{-}}{ }^{16} C _{7}$
$={ }^{16} C _{9}+{ }^{16} C _{10^{-}}{ }^{16} C _{10^{-}}{ }^{16} C _{9}=0$
$\left(\because{ }^{ n } C _{ r }={ }^{ n } C _{( n - r )}\right)$