Question

There are two girls Rina and Tina having $n_1$ and $n_2$ distinct numbers of toys respectively. The number of ways in which they can exchange their toys so that after exchanging they have the same number of toys with them but not the same toys, is

• A. ${}^{n_1+n_2}{C}_{n_1}$
• B. ${}^{n_1+n_2}{C}_{n_1}-1$
• C. ${}^{n_1+n_2}{P}_{n_1}$
• D. None of these

Answer 1

Answer: (B)

Let us mix the toys making $(n_1+n_2)$ number of distinct toys in all. Now, Rina can pick up $n_1$ toys out of these $(n_1+n_2)$ toys in ${}^{n_1+n_2}{C}_{n_1}$ ways which includes one way in which she can pick up her own original toys.
$\therefore$ Required number of ways ${}^{n_1+n_2}{C}_{n_1}-1$.