Notice that some of the layers are identical. We must take this into account when calculating the number of ways we can arrange them.
302 400
Practice makes perfect
We have a group of 10 layers and want to know how many ways they can be arranged. Notice that this is a permutation where two type of layers — the mashed avocado and cheddar cheese — occur multiple times. Therefore, we want to use the following formula.
n!/r_1!r_2!...
In this formula n is the number of items and r_1, r_2,... is the number of times that item 1, item 2, and so on, repeats. As already explained there are 10 layers, which means n= 10. Also, two layers occur three times and two times respectively. This means we have r_1= 3. and r_2= 2.
10!/3! 2!
Let's calculate this on a graphing calculator.
