Posted: 11/7/2002 1:20:19 PM EDT
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4 cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of 4 cards are possible? a)54145 b)6497400 c)270725 d)1082900 |
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there are 52 CARDS in a deck. regardless of the face. you only have 52. the 3 you mention are all the same. they only count as one 4 card set. if you try that pattern B is not enough and its the highest number. if you want to go that route multiply B by 16(4 cards * 4 places) 103958400 |
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There are 270725 unique [b]sets[/b]. A set has no ordering mathematically speaking, so the answer is "52 choose 4", which is 52!/48!/4! = 52*51*50*49/24 = 6497400/24 = 270725 Why? There are 52 choices for the first card, 51 for the second, 50 for the 3rd, 49 for the 4th. That's 6497400 ways. But there are duplicate sets; you have to count the number of ways to order 4 unique cards. Again: 4 choices for the first, 3 for the 2nd, 2 for the 3rd, and 1 for the 4th. That's 24 ways to order 4 unique cards, so you have to divide by 24 in order to not double-count your sets. If order really is important (so you're not really talking about sets), then the answer is 6497400. |