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Q. If $\, {{^n C}_{12}}$ =$\, {{^n C}_8}$ then $n$ is equal to

KCETKCET 2017Permutations and Combinations

Solution:

We know that.
If ${ }^{n} C_{x}={ }^{n} C_{y}$, then
(i) $x=y$
(ii) $x + y = n $
$ \therefore { }^{n} C_{12}={ }^{n} C_{8} $
$ \Rightarrow n=12+8=20$