Permutations and Combinations

There are 4 possibilities for inviting the relatives to the party:
3 ladies from the husband's side and 3 gentlemen from the wife's side:
Total number of ways:
=‌4C3×‌4C3=16
3 gentlemen from the husband's side and 3 ladies from the wife's side:
Total number of ways:
=‌3C3×‌3C3=1
2 ladies and 1 gentleman from the husband's side and 2 gentlemen and 1 lady from the wife's side:
Total number of ways:
=(‌4C2×‌3C1)×(‌3C1×‌4C2)=324
1 lady and 2 gentlemen from the husband's side, and 2 ladies and 1 gentleman from the wife's side:
Total number of ways:
=(‌4C1×‌3C2)×(‌3C2×‌4C1)=144
The total number of ways to invite 3 of the man's relatives and 3 of the wife's relatives is:
=16+1+324+144=485