possibilities-combination-how many ways,so that each man get married with one of the women

Question

I have a question.There is a group of 5 men and a group of 7 women.With how many ways can each of the 5 men get married with one of the 7 women?

score 2 · Accepted Answer · answered Dec 27 '13 at 20:18

2

Number of ways to choose $5$ out of $7$ woman:

$${7} \choose {5}$$

Number of ways to permute 5 woman to 5 man:

$$ 5!$$

All together:

$${7 \choose{5}}5! =2520 $$

answered Dec 27 '13 at 20:18

benh

6,605

1

And what if it is allowed that a woman can marry simultaneously as many men as she wants and all men have to marry,and the same man cannot be married with two women?? – evinda Apr 24 '14 at 23:33

score 2 · Answer 2 · answered Dec 27 '13 at 20:18

2

Assuming monogamy (No woman is married to more than one man), it is $$7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 = 2520$$ In general, it is for $n$ women and $k$ men $$P(n,k) = \frac{n!}{(n-k)!}$$

answered Dec 27 '13 at 20:18

AlexR

24,905

1

And what if it is allowed that a woman can marry simultaneously as many men as she wants and all men have to marry,and the same man cannot be married with two women?? – evinda Apr 24 '14 at 23:33
That trivially leaves us with $7^5$ possibilities – AlexR Apr 26 '14 at 17:40
Could you explain it further to me? :/ – evinda Apr 26 '14 at 17:52
Each man choses one woman, regardless of the other choices. – AlexR Apr 28 '14 at 18:00

score 2 · Answer 3 · answered Dec 27 '13 at 20:19

2

Line the men up in some order (the exact order doesn't make a difference). How many possible choices are there for the first man's wife? The second man's, once the first man's has been chosen? The third man's, once the first two men's have been chosen? Continue in this fashion and multiply the answers at each stage.

answered Dec 27 '13 at 20:19

Cameron Buie

102,994

1

For the first man can marry one of the 7 women,the second 6 women,the third 5 women,the fourth 4 women,and the fifth 3 women.So,it is 76543.Thanks for your answer!!! – evinda Dec 27 '13 at 21:34
1

And what if it is allowed that a woman can marry simultaneously as many men as she wants and all men have to marry,and the same man cannot be married with two women?? – evinda Apr 24 '14 at 23:34
It would be better to ask that as a separate question. I'm afraid I don't have time to address it. – Cameron Buie Apr 25 '14 at 11:35

possibilities-combination-how many ways,so that each man get married with one of the women

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