i had a question and its

"A man has 5 female and 7 male friends and his wife has 7 female and 5 male friends. In how many ways can they invite 6 males and 6 females if husband and wife are to invite 6 friends each? Answer. 267,148."

i tried to have cases by that each person invited six and total of 6 females and 6 males

1 = 5 mens * 1 female + 1 man * 5 females and cont

and then sum them up but the answer was less than the answer given it was 1848


closed as off-topic by xskxzr, Yuval Filmus, Apass.Jack, Evil, David Richerby Dec 31 '18 at 22:02

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about computer science, within the scope defined in the help center." – xskxzr, Yuval Filmus, Apass.Jack, Evil, David Richerby
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ This is a pure math question. $\endgroup$ – Yuval Filmus Dec 26 '18 at 5:34

Say the man invites 2 of his male friends so he has to invite 4 female friends to get to a total of 6. The female fills the gaps - she invites 4 male friends and 2 females. Now the guy has C(5,4) options to invite female friends and C(7,2) for his male friends in this example. The female has C(7,2) for the female part and C(5,4) for the male part.

Now you sum over all variants: sum


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