JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q66

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MathematicsSingle correct+4 / -1Question 66 of 90

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 :

468

469

484

485

Answer and worked solution

Official answer: D

If X invites $i$ ladies and $3-i$ men, Y must invite $3-i$ ladies and $i$ men. Each case counts $\left[\binom4i\binom3{3-i}\right]^2$ :
$1^2+12^2+18^2+4^2=1+144+324+16=485.$

Topics:Combinations

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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 66