SOLUTION: A man has 7 relative.Four of them are ladies and 3 gentleman;his wife also has 7 relatives.Three of them are ladies and 4 gentlemen.IN how many ways can they invite 3 ladies and 3

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Question 1135860: A man has 7 relative.Four of them are ladies and 3 gentleman;his wife also has 7 relatives.Three of them are ladies and 4 gentlemen.IN how many ways can they invite 3 ladies and 3 gentlmen for a dinner party so that there are 3 of the mans relatives and 3 of the wifes relatives?
Answer by VFBundy(438) About Me  (Show Source):
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Different combinations where you can choose three of the husband's relatives and three of the wife's relatives:

HUSBAND..............WIFE:
3 men.........................3 women
2 men/1 woman........1 man/2 women
1 man/2 women........2 men/1 woman
3 women....................3 men

Here are the number of ways you can choose each combination:

HUSBAND..............WIFE:
3 men.........................3 women = (3C3) * (3C3) = (1) * (1) = 1

HUSBAND..............WIFE:
2 men/1 woman........1 man/2 women = (3C2 * 4C1) * (4C1 * 3C2) = (3 * 4) * (4 * 3) = (12) * (12) = 144

HUSBAND..............WIFE:
1 man/2 women........2 men/1 woman = (3C1 * 4C2) * (4C2 * 3C1) = (3 * 6) * (6 * 3) = (18) * (18) = 324

HUSBAND..............WIFE:
3 women....................3 men = (4C3) * (4C3) = (4) * (4) = 16

Add all these together:
1 + 144 + 324 + 16 = 485

There are 485 different ways the couple can invite three men and three women to a dinner party so that three of the people are relatives of the husband and three of the people are relatives of the wife.