[JEE Advanced 1985] a man s 7 relatives are 4 ladies and 3 gentlemen his wife s
A man's $7$ relatives are $4$ ladies and $3$ gentlemen; his wife's $7$ are $3$ ladies and $4$ gentlemen. In how many ways can they invite $3$ ladies and $3$ gentlemen with $3$ from each side?
1 Answer
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· 2d ago
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Answer: $485$.
If the man supplies $a$ ladies and $3-a$ gentlemen (and the wife the rest), summing $\binom4a\binom3{3-a}\binom3{3-a}\binom4a$ over $a=0,1,2,3$ gives $1+144+324+16=485$.
JEE Advanced 1985 · Permutations and Combinations — verified solution by the Vidaara Team.
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