Permute and choose are counting functions. \u00a0Found on any scientific calculator, they look similar to\u00a0nPr<\/em> and\u00a0nCr<\/em>, respectively.<\/p>\n You use permutation (nPr)<\/em> to count the number of arrangements.<\/p>\n Example: \u00a0Eight people are posing in a row for a photograph. \u00a0How many ways can they be positioned?<\/p>\n Solution: \u00a0Assuming they are all in the photograph, the answer is 8P8<\/em>, which works out to 40 320 ways.<\/p>\n Example, Continued: \u00a0What if only 5 of the 8 people are going to be in the photograph?<\/p>\n Solution: \u00a0Now, the answer is 8P5: \u00a0<\/em>6720 ways.<\/p>\n You use combination (nCr<\/em>) 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.<\/p>\n Example: \u00a0How many ways can you select three crayons from a box of 12?<\/p>\n Solution: \u00a012C3,\u00a0<\/em>or 220 ways.<\/p>\n With choose, the order of the selection doesn’t matter – just which items are selected. With permute, the order of the items matters.<\/p>\n Both permute and choose are \u00a0without replacement<\/i> – which means that once an object is placed or selected, it can’t “come up” again. \u00a0This only makes sense: \u00a0a person can’t show up in two different places in the same photograph. \u00a0Similarly, 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.<\/p>\n Other counting strategies will be discussed in future posts:)<\/p>\n