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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?
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TeeEm
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(Original post by TSRforum)
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?
Good problem ... my homework for tomorrow
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(Original post by TeeEm)
Good problem ... my homework for tomorrow
Good night
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Good night
you too
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Gregorius
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(Original post by TSRforum)
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?
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TeeEm
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(Original post by TSRforum)
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?
I got 63 committees
(Hope it is right)
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username1732491
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(Original post by TSRforum)
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?
I got 63 committees as well.
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(Original post by Gregorius)
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?
Still confused...
All I did was (4C1 x 5C2) + (4C2 x 5C1) = 70 then subtracted 4C1 and 5C1 which gives me 60. Though how am I suppose to know which combos include a married couple? And if I subtract these off I would get an answer less than 63.


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