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 52-card 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 ﬁve-card hands that can be drawn from a full deck, there are only ( 20 5 ) = 15,504 diﬀerent ﬁve-card hands that can be drawn from this smaller deck. How many of the ﬁve-card hands that can be drawn from this 20-card 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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