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In a conference of $8$ persons,if each person shakes hands with every other person exactly once,then the total number of handshakes is:

$^nC_{r+1} + ^nC_{r-1} + 2^nC_r = \dots$

Difficult
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If $\binom{n+1}{3} = 2 \times \binom{n}{2}$,then $n = \dots$

In how many ways can Rs. $16$ be divided among $4$ persons if none of them gets less than Rs. $3$?

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Compute $\frac{12!}{10! \times 2!}$

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