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.

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

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.

To explain this problem to your son, you can use a visual approach. You can set up a grid with rows representing the different chores and columns representing the different weeks. Each cell in the grid will represent a specific combination of the chores for a given week.

Here's how you can set it up:

1. Create a grid with 4 rows (for the 4 chores) and as many columns as the number of weeks you want to consider. Let's say we are considering 4 weeks for this example.

2. Label the rows with the names of the chores - "Empty Trash," "Water Plants," "Fill Bird Feeder," and "Sort Recycling."

3. List the weeks numbers in the top row of the grid, from 1 to 4.

4. Now, you can start filling in the cells of the grid. Each cell represents a specific combination of chores for a given week.

- For the first chore, "Empty Trash," start with the first week and fill in "Empty Trash" in the corresponding cell.

- For the second chore, "Water Plants," move to the next week and fill in "Water Plants" in the corresponding cell. As you go across the weeks, continue filling in the second chore.

- Repeat this process for the remaining chores, until you have filled in all the cells in the grid.

5. Once you have filled in all the cells, count the number of different ways Sam can complete his chores by counting the number of unique combinations.

For example, let's say Sam has 4 weeks and he wants to complete all chores every week. The grid might look like this:

Weeks: 1 2 3 4
------------------------------
Chore 1: | X | X | X | X |
Chore 2: | X | X | X | X |
Chore 3: | X | X | X | X |
Chore 4: | X | X | X | X |

In this case, there is only one way to complete his chores each week - he has to complete all of them.

However, if he wants to add variety, you can discuss with your son how he can mix and match the chores in different ways. Encourage him to explore the different combinations by changing which chores he does each week. The number of different ways will depend on how he chooses to mix up the chores.

I hope this explanation helps! Feel free to ask if you have any further questions.