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

  • $\begingroup$ 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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