invite 12 person from 24 that we have 6 men and 6 womens 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
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: