# A club consists of $6$ men and $5$ women.? [closed]

How many ways can a president and a vice-president be chosen if they cannot be both men or both women?

## closed as off-topic by SBareS, JMP, P Vanchinathan, zhoraster, user91500Mar 16 '17 at 6:18

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• Choose one man and one woman, then select which of them will be president. – Henning Makholm Mar 15 '17 at 16:06
• Hint: How many ways can you choose a male president and a female vice-president? – robjohn Mar 15 '17 at 16:06
• There are 6 ways to pick a man and 5 ways to pick a woman. Then there is one more choice: whom of them gets which post. – mathreadler Mar 15 '17 at 16:07

$$\underset{\text{Pres}}{\binom 51}\underset{\text{VP}}{\binom 61} + \underset{\text{Pres}}{\binom 61}\underset{\text{VP}}{\binom 51} = 5\cdot 6 + 6\cdot5 = 30+30=60$$
Note $\binom xy$ ("$x$ choose $y$") are binomial coefficients.
Total number of ways $$=\dbinom61 \times \dbinom51 \times 2!$$ $$=60~\text{ways}$$