Tom, Tristan, Luca, and Pablo are lined up and ready to be picked for kickball teams. How many different ways can they be picked from first to last?
We could list the ways, but that isn't necessary now that we know about awesome factorials.
The number of ways to pick the four boys is 4! = 4 × 3 × 2 × 1 = 24.
If all boys were picked in a random order, what is the probability that Tom will luck out and be picked first?
To answer the probability question we need to look at all the ways that Tom could be picked first. Here they are:
If we fix Tom as the kid picked first, and arrange the other three, we find 6 different ways, which is 3!.
3! = 3 × 2 × 1 = 6
So the probability that Tom is picked first is 6 out of a possible 24 combinations. The probability is: