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Posted: 11/7/2002 1:20:19 PM EDT
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
Link Posted: 11/7/2002 1:59:43 PM EDT
A
Link Posted: 11/7/2002 2:08:56 PM EDT
B. Arrival? 52*51*50*49 the number lessens each time because there is one less card in the deck on each draw.
Link Posted: 11/7/2002 2:19:18 PM EDT
Originally Posted By NOVA5: B. Arrival? 52*51*50*49 the number lessens each time because there is one less card in the deck on each draw.
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That was my first guess as well. However, that doesn't take into account duplicate sets. AH, KH, QH, JH = KH, AH, QH, JH = JH, AH, KH, QH, etc
Link Posted: 11/9/2002 1:54:45 PM EDT
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
Link Posted: 11/9/2002 2:14:05 PM EDT
[Last Edit: 11/9/2002 2:15:05 PM EDT by fizassist]
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.
Link Posted: 11/9/2002 2:41:41 PM EDT
your right, it is 24 not 16. the funny thing is that this question, depending on the rules of the answer can be any of the 4.
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