Combinations Question

A committee of 3 is to be selected from 4 women and 5 men. Atleast 1 man and 1 women must be on the committee. One of the men and one of the women marry each other. Rules also state married couples may not both serve on the committee. How many ways can the committee be chosen?

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A committee of 3 is to be selected from 4 women and 5 men. Atleast 1 man and 1 women must be on the committee. One of the men and one of the women marry each other. Rules also state married couples may not both serve on the committee. How many ways can the committee be chosen?

A committee of 3 is to be selected from 4 women and 5 men. Atleast 1 man and 1 women must be on the committee. One of the men and one of the women marry each other. Rules also state married couples may not both serve on the committee. How many ways can the committee be chosen?

A committee of 3 is to be selected from 4 women and 5 men. Atleast 1 man and 1 women must be on the committee. One of the men and one of the women marry each other. Rules also state married couples may not both serve on the committee. How many ways can the committee be chosen?

Break this down into parts:

(i) How many ways are there of choosing a committee of 3 from 5 + 4 people?
(ii) How many of the combinations that you found in part (i) consist entirely of men or entirely of women? Subtract these off.
(iii) How many of the combinations that you found in (i) include a married couple? Is it OK to subtract these off? Why?