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1. 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?

A. 9

B. 30

C. 36

D. 15

Solution:

There are 6 candidates and a voter has to vote for any two of them.
So, the required number of ways is,

\begin{aligned} =^{6} C_{2} \\ = \frac{6!}{2! \times 4!} \\ = 15 \end{aligned}

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