With counting problems, the math tutor needs to explain the uses of permute and choose.

Permute and choose are counting functions.  Found on any scientific calculator, they look similar to nPr and nCr, respectively.

You use permutation (nPr) to count the number of arrangements.

Example:  Eight people are posing in a row for a photograph.  How many ways can they be positioned?

Solution:  Assuming they are all in the photograph, the answer is 8P8, which works out to 40 320 ways.

Example, Continued:  What if only 5 of the 8 people are going to be in the photograph?

Solution:  Now, the answer is 8P5:  6720 ways.

You use combination (nCr) to count the number of assortments – that is, the number of ways you can select a set of r objects from a set of n objects.

Example:  How many ways can you select three crayons from a box of 12?

Solution:  12C3, or 220 ways.

With choose, the order of the selection doesn’t matter – just which items are selected. With permute, the order of the items matters.

Both permute and choose are  without replacement – which means that once an object is placed or selected, it can’t “come up” again.  This only makes sense:  a person can’t show up in two different places in the same photograph.  Similarly, if you are using only one deck of cards, you can’t receive the queen of hearts, then receive it a second time in the same hand.

Other counting strategies will be discussed in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.