JEE Main · 2017 · 02 Apr 2017 · Offline · Permutations and Combinations

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 :

(A)484
(B)485✓ Correct
(C)468
(D)469

Answer: (B)

Solution

We want three ladies and three men at the party, with exactly three guests drawn from each host's own circle. Sorting by how the ladies divide between the two sides, the four workable cases contribute

16

324

144

and

1

ways, and together they give

16 + 324 + 144 + 1 = 485

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option

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