Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote?

Three gentlemen and three ladies are candidates for two vacancies. A voter has to vote for two candidates. In how many ways can one cast his vote? Correct Answer 15

There are 6 candidates and a voter has to vote for any two of them. So, the required number of ways is,$$\eqalign{ & { = ^6}{{\text{C}}_2} \cr & = \frac{{6!}}{{2! \times 4!}} \cr & = 15 \cr} $$
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