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  4. If nC3=220, then n equals to:

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Q. If $ ^{n}{{C}_{3}}=220, $ then n equals to:

KEAMKEAM 2003

Solution:

$ ^{n}{{C}_{3}}=220 $ $ \Rightarrow $ $ \frac{n!}{(n-3)!3!}=220 $ $ \Rightarrow $ $ n(n-1)(n-2)=220\times 6 $ $ \Rightarrow $ $ n(n-1)(n-2)=12(12-1)(12-2) $ $ \Rightarrow $ $ n=12 $