The given information is:
- There are 3 children
- Each of the children will be allowed to select one box from the 10 different boxes of cereal available
- All the boxes are different
The number of ways the boxes can be selected n= 10!=10x9x8x7x6x5x4x3x2x1
The number of ways the 3 children can choose r= 3!=3x2x1
Here we have a permutation without repetition, because we have to reduce the options each time, so the formula is:

If we replace n=10 and r=3, we obtain:

The answer is 720.