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  4. If nC12=nC8, then value of nC19 is

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Q. If $ ^{n}{{C}_{12}}{{=}^{n}}{{C}_{8}}, $ then value of $ ^{n}{{C}_{19}} $ is

Rajasthan PETRajasthan PET 2009

Solution:

Given, $ ^{n}{{C}_{12}}{{=}^{n}}{{C}_{8}} $
$ \Rightarrow $ $ \frac{n!}{(n-12)!12!}=\frac{nQ}{(n-8)!8!} $
$ \Rightarrow $ $ (n-8)(n-9)(n-10)(n-11) $
$ =12\times 11\times 10\times 9 $
$ \Rightarrow $ $ n-8=12\Rightarrow n=20 $
$ \therefore $ $ ^{20}{{C}_{19}}=20 $