The value of $^{n} C_{r} -$ $^{n} C_{n - r} =$ ______________.

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Solution

Consider $^{n} C_{r} -^{n} C_{n - r}$
$= \frac{n!}{(n - r)! r!} - \frac{n!}{(n - (n - r))! (n - r)!}$
$= \frac{n!}{(n - r)! r!} - \frac{n!}{r! (n - r)!}$
$= 0$
Hence, $^{n} C_{r} -^{n} C_{n - r} = 0$ .

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