tanmay056 wrote:

I am not sure if - 5C2 is going to be correct one .... It seems to me that 5C3 is going to be more precise answer. Because we need to select group of 3 people out of 5. Though both of them will result in 10 . Please clarify of choosing 5C2 over 5C3.

\(5C2 = 5C3\)

Note that \(C^k_n =\frac{n!}{k!(n-k)!}\)

\(C^{n-k}_n=\frac{n!}{(n-k)!(n-(n-k))!}=\frac{n!}{(n-k)!k!}\)

Hence \(C^k_n = C^{n-k}_n\)

That's why \(C^3_5 = C^2_5\)

Now let's compare \(5C2\) vs \(5C3\).

If you choose 3 out of 5, there are \(5C3\) different ways.

If you choose 3 out of 5, that means you drop 2 of 5 and 3 left. Thus there are \(5C2\) different ways.

Two different ways with different concept, but have the same result. So you could choose any one which suits you.

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