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  4. A man has 7 relatives, 4 of them are ladies and 3 gentlemen; his wife has 7 relatives and 3 of them are ladies and 4 gentlemen. The number of ways they can invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of men's relatives and 3 of wife's relatives is

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Q. A man has $7$ relatives, $4$ of them are ladies and $3$ gentlemen; his wife has $7$ relatives and $3$ of them are ladies and $4$ gentlemen. The number of ways they can invite a dinner party of $3$ ladies and $3$ gentlemen so that there are $3$ of men's relatives and $3$ of wife's relatives is

Permutations and Combinations

Solution:

The scheme is as follows
image
Total number of ways $=1+144+324+16=485$