Permutations and CombinationsDate: 03/11/98 at 16:06:18 From: Andrew Demers Subject: Permutations and Combinations - What's the Difference? I am a student at Hershey Middle School. Recently I was working with my math teacher on combinations and permutations. He admitted that it was not a strong point of his and e were both wondering what the difference is between the two things. Thanks in advance. Andrew Demers Date: 03/12/98 at 15:33:01 From: Doctor Daniel Subject: Re: Permutations and Combinations - What's the Difference? Hi there, Good question! The difference concerns whether the order of the objects matters, more or less. In a permutation, the order does matter, while in a combination, all that matters is which set of objects was chosen. Here's an example: Suppose you have eight objects, labeled A through H. Then the number of permutations of 5 of these eight objects is 8x7x6x5x4; there are eight possibilities for the first, seven for the second, and so on. And the permutation ACHED is different from HEADC. For combinations, there are far fewer; here we're really asking how many subsets of 5 objects of the original eight there are. It shouldn't be too hard to convince yourself that there are 120 times fewer combinations than permutations. Why? Well, consider that ALL permutations that include the letters FACDE are really part of the same combination, {A,C,D,E,F}. And there are 120 = 5! = 5x4x3x2x1 of them. Here are another couple of tidbits: The number of combinations of K objects chosen from a set of N is equal to N!/K!(N-K)!, while the number of permutations is just N!/(N-K)! Also, why is it that there are exactly the same number of combinations of 5 letters out of 8 as there are of 3 letters out of 8 (don't just say "the formula tells me so...") -Doctor Daniel, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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