Permutations, Combinations, and Random Numbers on the TI83 Plus
You can use the TI83 Plus to evaluate a permutation or combination. 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?” 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?”
To evaluate a permutation or combination, follow these steps:

On the Home screen, enter n, the total number of items in the set.
If you’re not already on the Home screen, press [2nd][MODE] to exit (quit) the current screen and enter the Home screen.

Press
to access the Math Probability menu.

Press [2] to evaluate a permutation or press [3] to evaluate a combination.

Enter r, the number of items selected from the set, and press [ENTER] to display the result.
Notice that the last two lines in the figure tell you that it’s impossible to select 7 items from a set of only 5 items.
Generate random integers on the TI83 Plus
When generating random numbers, you usually want to generate numbers that are integers contained in a specified range, or decimal numbers that are strictly between 0 and 1. To generate random integers that fall between the integers a and b:

Press
to select the randInt command from the Math Probability menu.

Enter the value of the lower limit a, press [,], and enter the upper limit b.

Press [ENTER] to generate the first random integer. Repeatedly press [ENTER] to generate more random integers.
Pressing any key except [ENTER] stops the calculator from generating random integers.
Generate random decimals on the TI83 Plus
To generate random decimal numbers that are strictly between 0 and 1, press
to select the rand command from the Math Probability menu. Then repeatedly press [ENTER] to generate the random numbers.