# Difficult Permutation-Combination Solved QuestionAptitude Discussion

 Q. If $F(x, n)$ be the number of ways of distributing $x$ toys to $n$ children so that each child receives at the most $2$ toys then $F(4, 3) =$ _______?
 ✖ A. $3$ ✖ B. $4$ ✖ C. $5$ ✔ D. $6$

Solution:
Option(D) is correct

We have to find the number of ways in which 4 toys can be distributed to 3 children so that each child receives at the most 2 toys.

There are two possible cases:

Case 1:

Two of them receive 2 toys each and one of them doesn’t get any toy.

There are 3 possible ways to distribute the toys in this case i.e., the three possible ways of selecting the child who will not get any toy.

Case 2:

Two of them receive 1 toy each and one of them receives 2 toys.

Again there are 3 possible ways to distribute the toys in this case i.e., the three possible ways of selecting the child who will get 2 toys.

So there are a total of $\textbf{6}$ possible ways.