HP 35s Instruction Manual page 2

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HP 35s Probability – Rearranging items
Rearranging items
There are a great number of applications that involve determining the number of ways a group of items can be
rearranged. The factorial function, accessed by pressing º* (which is the right-shifted function of the / key) on
the 35s, will determine the number of ways you can rearrange the total number of items in a group. Note that the 35s will
interpret the factorial function as the gamma function if the argument for the function is a non-integer real number. The
permutation function, accessed by pressing º{ (which is the right-shifted function of the ¸ key), will return the
number of ways you can select a subgroup of a specified number of items from a larger group, where the order of each
of the items in the subgroup is important. The combination function, accessed by pressing ¹x (which is the left-
shifted function of the ¸ key), will return the number of ways you can select a subgroup of a specified number of items
from a larger group, where the order of each of the items in the subgroup is not important.
To see the difference between permutations and combinations, consider the set of three items A, B, and C. If we select a
subgroup of 2 items, we could select AC and CA as two possible subgroups. These would be counted as different
subgroups if computing the number of permutations, but only as one subgroup if computing the number of combinations.
Note that the factorial function operates the same in algebraic mode as it does in RPN mode. The number is keyed in
and then the factorial function is selected from the keyboard. For permutations and combinations in RPN mode, the two
numbers must be entered into the first two levels of the stack and then the function is selected from the keyboard. In
algebraic mode, permutations and combinations require the function to be selected, then the first number to be keyed in
and then the second number keyed in followed separated from the first by a 35s supplied comma followed by pressing
the Ï key to evaluate the function.
Factorials show up throughout mathematics and statistics. Permutations and combinations show up in many discrete
probability distribution calculations, such as the binomial and hypergeometric distributions.
Practice solving problems involving factorials, permutations, and combinations
Example 1: How many different ways could 4 people be seated at a table?
Solution: In RPN or algebraic mode: 4º*
Answer: 24. Figure 1 shows the display assuming RPN mode.
Example 2: How many different hands of 5 cards could be dealt from a standard deck of 52 cards? Assume the
order of the cards in the hand does not matter.
Solution: Since the order of the cards in the hand does not matter, the problem is solved as a Combination.
In RPN mode: 52Ï5¹x
In algebraic mode: ¹x52Õ5Ï
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Figure 1
Figure 2
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