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Permutations and Combinations and the TI-84 Plus

You can work permutations and combinations on the TI-84 Plus calculator. A permutation, denoted by nPr, answers the question: “From a set of n different items, how many ways can you select and order (arrange) r of these items?” One thing to keep in mind is that order is important when working with permutations.

Permutation questions may ask questions like, “In how many ways could ten runners end up on the Olympic medal stand (Gold, Silver, or Bronze)?" Is order important? Yes; use nPr with n = 10 and r = 3).The formula for a permutation is: nPr = (n!)/(n-r)!

A combination, denoted by nCr, answers the question: “From a set of n different items, how many ways can you select (independent or order) r of these items?” Order is not important with combinations.

Combination questions may look like, “A subcommittee made up of 4 people must be selected from a group of 20.” Is order important? No; the five committee positions are equally powerful. Use nCr with n = 20 and r = 4. The formula for a combination is: nCr = (n!)/(r!(n-r)!).

Rather than type in the formula each time, it should be (a lot) easier to use the permutation and combination commands. To evaluate a permutation or combination, follow these steps:

  1. There are two ways to access the nPr and nCr templates: Press

    image0.jpg

    to access the Math PROB menu or press [ALPHA][WINDOW] to access the shortcut menu.

    On the TI-84 Plus, press

    image1.jpg

    to access the probability menu where you will find the permutations and combinations commands. Using the TI-84 Plus, you must enter n, insert the command, and then enter r.

    See the PROB menu in the first screen. See the shortcut menu in the second screen. Press the number on the menu that corresponds to the template you want to insert.

    image2.jpg
  2. In the first blank, enter n, the total number of items in the set.

    Alternatively, you could enter n first and then insert the template.

  3. Press the right-arrow key to navigate your cursor to the second blank in the template.

  4. Enter r, the number of items selected from the set, and press [ENTER] to display the result.

    See the last screen. Notice the blank nPr template in the last line of the last screen.

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