Question
A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends,3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is
-
484
-
485
-
468
-
469
Solution
B.
485
Total number of ways
4C0 · 3C3 · 3C3 · 4C0 + 4C1 · 3C2 · 3C2 · 4C1 + 4C2 · 3C1 · 3C1 · 4C2 + 4C3 · 3C0 · 3C0 · 4C3= 485
