Permutation-Combination
Aptitude

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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.

$6$

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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.


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