HP 10s Instruction Manual page 3

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HP 10s Probability – Rearranging Items
Practice solving problems involving factorials, permutations, and combinations
Example 1: Calculate the number of combinations and permutations of 15 objects taken 5 at a time.
Solution: The number of combinations is calculated by first keying in the value of n (it can be the result of a
calculation) then pressing F and finally keying the value of r. = displays the result:
15 F5=
Likewise, the number of permutations is calculated by pressing:
15 Ac 5=
Answer: 3003 and 360360.
Example 2: Calculate the number of ways that six people can line up for a photograph.
Solution: Since the order does matter in this example, the problem is solved as a permutation:
6 Ac 6=
P
Note that
which is a postfix function on the HP 10s:
6 A b
The = key is not required now, because the result of a postfix function is automatically displayed as soon
as its key is pressed.
Answer: 720
Example 3: In how many different ways can five seats be filled by a group of ten persons?
Solution: Again, the order is important ,so the answer is
10 Ac5 =
Answer: 30,240
Example 4: 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:
52 F 5=
hp calculators
6
= !
6 6 5 4 3
= ! ! ! !
6
2 1
, so this example can be solved using the factorial function,
!
10
P
. Press
5
- 3 -
6
P
. Press:
6
HP 10s Probability – Rearranging Items - Version 1.0
52
C
5