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CSE 260
SOLUTIONS TO YELLOW QUIZ 7
Spring 2007
INSTRUCTIONS: When your answer includes a product of integers, multiply them out.
1. [4 points] Suppose that we take a 52card deck of cards and throw away all of the cards except aces, kings,
queens, jacks, and tens. We are left with a deck of cards containing just 5 denominations and 4 suits, for a
total of 20 cards instead of 52. Instead of
(
52
5
)
= 2,598,960 diﬀerent ﬁvecard hands that can be drawn from a
full deck, there are only
(
20
5
)
= 15,504 diﬀerent ﬁvecard hands that can be drawn from this smaller deck.
How many of the ﬁvecard hands that can be drawn from this 20card deck would count as two pairs in poker
(two cards of one denomination, two cards of a second denomination, and a ﬁfth card of a third denomination)?
If you do it the way the book did in Example 6.4.9, you would get
±
5
2
²±
4
2
²±
4
2
²±
12
1
²
=10
×
6
×
6
×
12 =
4,320
hands. Or you could calculate the number of ways to pick two denominations for the two pairs and a
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 Spring '07
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