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Question: Answered & Verified by Expert
7 relatives of a man comprise 4 ladies and 3
gentlemen. His wife also has 7 relatives − 3 of
them are ladies and 4 are gentlemen. In how
many ways can they invite a dinner party of
3 ladies and 3 gentlemen, so that there are
3 of man’s relative and 3 of wife’s relative?
MathematicsPermutation CombinationAP EAMCETAP EAMCET 2021 (25 Aug Shift 2)
Options:
  • A 485
  • B 500
  • C 486
  • D 102
Solution:
1109 Upvotes Verified Answer
The correct answer is: 485



$\therefore$ Number of ways to invite a dinner party of 3 ladies and 3 gentlemean, so that there are 3 of man's relative and 3 of wife's relative
$$
\begin{aligned}
& ={ }^3 C_3 \cdot{ }^3 C_3+{ }^3 C_2 \cdot{ }^4 C_1 \times{ }^4 C_1{ }^3 C_2+{ }^3 C_1{ }^4 C_2 \cdot{ }^4 C_2 \cdot{ }^3 C_1 \\
& \\
& \quad+{ }^4 C_3 \cdot{ }^4 C_3 \\
& =1+3 \cdot 4 \cdot 4 \cdot 3+3 \cdot 6 \cdot 6 \cdot 3+4 \cdot 4 \\
& =1+144+324+16 \\
& =485
\end{aligned}
$$

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