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  4. If n2-n C2= n2-n C10, then n=

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Q. If $^{n^{2}-n} C_{2}={ }^{n^{2}-n} C_{10},$ then $n=$

Binomial Theorem

Solution:

${ }^{n^{2}-n} C_{2}={ }^{n^{2}-n} C_{10} $
$\Rightarrow { }^{n^{2}-n} C_{n^{2}-n-2}={ }^{n^{2}-n} C_{10}$
$\Rightarrow n^{2}-n-2=10$ or $n=4,-3 .$