Question

A man has $7$ relatives, $4$ of them are ladies, and $3$ gentlemen; his wife has also $7$ relatives, $3$ of them are ladies and $4$ gentlemen. In how many ways can they invite a dinner party of $3$ ladies and $3$ gentlemen so that there are $3$ of them are man's relatives and $3$ of them are wife's relatives?

Answer 1

The four possible ways of inviting $3$ ladies and $3$ gentlemen for the party with the help of the table.
$\therefore$ Required number of ways to invite $=1+144+324+16=485$