(a) `C_2^5 times C_3^7` ` =frac{5!}{2! times 3!} times frac{7!}{3! times 4!}` ` = 350`

(b) `C_2^5 times C_2^6` ` =frac{5!}{2! times 3!} times frac{6!}{2! times 4!}` ` = 150`

(c) `C_2^3 times C_3^7 ` `=frac{3!}{2! times 1!} times frac{7!}{3! times 4!}` ` = 105`