A man has friends: ladies and men

MATHEMATICS · Single correct · CBSE · Mathematics · Permutations and Combinations · Permutations and Combinations

Problem

A man

X

has

7

friends:

4

ladies and

3

men. His wife

Y

also has

7

friends:

3

ladies and

4

men. Assume

X

and

Y

have no common friends. Find the total number of ways

X

and

Y

together can throw a party inviting

3

ladies and

3

men, such that

3

friends of each of

X

and

Y

are in the party. (1) 484 (2) 485 (3) 468 (4) 469