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?

Saketh May 20, 2019

#1**+2 **

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

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

.Rom May 20, 2019

#1**+2 **

Best Answer

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

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

Rom May 20, 2019