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# help

+1
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+40

A club with five men and six women wish to form a committee. The number of men must be between 1 and 3 (inclusive), and the number of women must be between 2 and 4 (inclusive). How many different committees can be formed?

May 20, 2019

#1
+5662
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I think we have to break it down into every possible case regarding the numbers of men and women on the committee.

$$\text{If there are m men and w women on the committee we have}\\ n_{m,w}=\dbinom{5}{m}\dbinom{6}{w} \text{ ways to select the committee from the members}\\~\\ N= \sum \limits_{m=1}^3\sum \limits_{w=2}^4 \dbinom{5}{m}\dbinom{6}{w}=1250$$

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May 20, 2019

#1
+5662
+2
$$\text{If there are m men and w women on the committee we have}\\ n_{m,w}=\dbinom{5}{m}\dbinom{6}{w} \text{ ways to select the committee from the members}\\~\\ N= \sum \limits_{m=1}^3\sum \limits_{w=2}^4 \dbinom{5}{m}\dbinom{6}{w}=1250$$