Counting Ii Statistics Worksheet Page 2
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9n!
We saw in the previous chapter that there are exactly
ways to choose
(n k)!
and order k objects from a set of n objects. Therefore,
n
n!
k! =
k
(n
k)!
Dividing the previous equation by k!:
n
n!
=
k
k!(n
k)!
Examples.
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• There are
di↵erent ways to choose which 3 of the 7 pairs of shorts
3
that you will take on your vacation.
7
7!
7(6)(5)(4!)
7(6)(5)
=
=
=
= 7(5) = 35
3
3!(7
3)!
3!4!
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• How many 5 card poker hands are there if you play with a standard
deck of 52 cards?
You’re counting the number of di↵erent collections of 5 cards that can be
taken from a set of 52 cards. This number is
52
52!
52(51)(50)(49)(48)(47!)
52(51)(50)(49)(48)
=
=
=
5
5!(52
5)!
5! 47!
5!
52(51)(50)(49)(48)
=
= 2, 598, 960
120
• You are in a small library. You want to check out 3 books. The
3287
library has 3287 di↵erent books to choose from. There are
di↵erent
3
collections of three books that you could check out.
3287
3287!
3287(3286)(3285)(3284!)
3287(3286)(3285)
=
=
=
3
3!(3287
3)!
3! 3284!
3!
35, 481, 554, 370
=
= 5, 913, 592, 395
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