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?

Step-by-step solution

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 aligned & = ^3 C₃ ^3 C₃+ ^3 C₂ ^4 C₁ ^4 C₁ ^3 C₂+ ^3 C₁ ^4 C₂ ^4 C₂ ^3 C₁ & & + ^4 C₃ ^4 C₃ & =1+3 4 4 3+3 6 6 3+4 4 & =1+144+324+16 & =485 aligned