Question

Please help not sure how to explain to my son. How should I set this up.

Sam has the same chores each week, but he wants to add variety. Suppose Sam has to empty trash, water the plants, fill the bird feeder, and sort the recycling. How many different ways can Sam complete his chores.

Answer 1

5*4*3*2*1=120 ways

Answer 2

Sam has 4 chores to complete - he can choose the order. He has 4 choices for the first chore.

For each choice of the first, he can choose 1 of the 3 remaining for the second chore.

etc.

4*3*2*1 = 24

This is more generally known as the ordering problem -- there are n! ways to order n objects.