Factorials, Permutations, and Combinations
In probability calculations, you often need to multiply a series of consecutive numbers (factorials) or find the number of possible arrangements of items (permutations or combinations). The functions discussed in this section provide you with these capabilities.
Factorial
The factorial function enables you to calculate the factorial of negative or positive numbers.The range of negative numbers is from -70.5 to 0. Only half-integer numbers are valid. For example, -8.5 and -9.5 are valid inputs, but -9 is not.
The factorial of any number less than -70.5 results in an answer of 0., indicating an underflow, due to the limit of 13 digits in the mantissa.
The valid range of positive numbers is from 0 to 69.5. Both half- and whole-integer numbers are valid. For example, 8.5, 9, and 9.5 are all valid inputs.
The factorial function operates on the internal value, not the displayed value. Use the [ 2nd ][ 13d ] key sequence to ensure a displayed number is a valid input.
Example
The following example illustrates the operation of the factorial function.Procedure | Press | Display |
|---|---|---|
| Clear display | [ CLEAR ] |  |
| Calculate -49.5 factorial | 49.5 [ +/- ] [ 2nd ] [ x! ] |  |
| Calculate -49 factorial | 49 [ +/- ] [ 2nd ] [ x! ] |  |
| Calculate 49 factorial | [ CLEAR ] 49 [ 2nd ] [ x! ] |  |
| Calculate 9.999999999 divided by 2 | 9.999999999 [ ÷ ] [ 2 ] [ = ] |  |
| Calculate the factorial | [ 2nd ] [ x! ] |  |
| Clear display | [ CLEAR ] |  |
Permutations
This function enables you to calculate the number of permutations of n items taken r at a time. The range is limited only by the range of the calculator as long as n is a positive number equal to or greater than r. If your calculation exceeds the range of the calculator, an "OVERFLOW" message appears.Example
Calculate the number of possible arrangements of six appliances of the same width on a kitchen wall with only room for three.Procedure | Press | Display |
|---|---|---|
| Clear display | [ CLEAR ] |  |
| Calculate the permutations | 6 [ x~t ] 3 [ 2nd ] [ nPr ] |  |
Combinations
This function enables you to calculate the number of combinations of n items taken r at a time. The range is limited only by the range of the calculator as long as n is a positive number equal to or greater than r. If your calculation exceeds the range of the calculator, an "OVERFLOW" message appears.Example
Calculate the number of hands you might draw from a deck of 52 cards if you draw 5 cards each time.Procedure | Press | Display |
|---|---|---|
| Clear display | [ CLEAR ] |  |
| Calculate the permutations | 52 [ x~t ] 5 [ 2nd ] [ nCr ] |  |
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