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  4. If nC9= nC8, find nC17.

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Q. If $ ^{n}C_{9}= \,{}^{n}C_{8}$, find $^{n}C_{17}$.

Permutations and Combinations

Solution:

$ ^{n}C_{p}= \,{}^{n}C_{k} $
$\Rightarrow n= p + k $
$ \therefore \,{}^{n}C_{9} = \,{}^{n}C_{8 } $
$\Rightarrow n= 9 + 8 =17 $
Now $^{17}C_{17} = 1 $