# Number of ways that seven toys can be distributed

1. Apr 4, 2016

### NihalRi

1. The problem statement, all variables and given/known data
Find the number of ways in which seven different toys can be given to three children, if the youngest vis to receive three and the others two.

2. Relevant equations

3. The attempt at a solution
7 combination 3 × 4 combination 2 × 2 combination 2
= 210
Is this the correct way of doing this question?

2. Apr 4, 2016

### PeroK

If you calculate it the other way round, starting with one of the children that gets two toys, do you get the same answer?

3. Apr 4, 2016

### NihalRi

Yes still 210, hoping this means it's right?

4. Apr 4, 2016

### PeroK

It's a good sign! Yes, it's right!

5. Apr 4, 2016

### Ray Vickson

It is OK, but another way (maybe easier?) is: C(7,3) = number of different ways of giving the youngest 3 toys. That leaves 4 toys to be distributed, 2 each to the other two, and the number of different ways of doing that (with the given leftover four toys) is C(4,2). Altogether, the number of ways is C(7,3)*C(4,2) = 210.