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?

Answer: Option D

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