7 relative of a man comprises 4 ladies and 3 gentlmen; his wife has also 7 relatives; 3 of them are ladies & 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man’s relative and 3 of the wife’s relative

(Q). 7 relative of a man comprises 4 ladies and 3 gentlmen; his wife has also 7 relatives; 3 of them are ladies & 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man’s relative and 3 of the wife’s relative?
Solution:-
This question can be solved by making different cases given below:-

Hence total number of ways = 16 + 1 + 144 + 324
                                                   = 485 ways         Answer