Question

Rekha married Shivram and had 4 sons. Versha married Ajay and had $4$ sons. Both the couples had divorce and after that shivram married versha. while Ajay married Rekha. They too had 3 sons each from their wedlocks. How many selections of $8$ children can be made from the $14$ child so that each of them have an equal number of sons in the selections?

Answer 1

Considering four groups $\to RS,VA,AR,VS$

Sons are $4,4,3,3$ respectively

So, $2$ from each will result in

No. of ways $=4_{C_2}\times 4_{C_2}\times 3_{C_2}\times 3_{C_2}=324$