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Permutations

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by diederiksmits
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Discipline:
Math
Subject:
Algebra I
Grade:
10

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Permutations

Period 3May 28, 2012Group: Diederik Smits, Jose Pablo Rueda, Seungmi Ha, and Max Monical

What are permutations?A permutation, also called an "arrangement number" or "order," is a rearrangement of the elements of an ordered list into a one-to-one correspondence with itself.Two types: Formulas:* With Repetition * n^r* Without Repetition * P(n,r)=n!/(n-r)!-n is the number of things to choose from, and you choose r of them-

PERMUTATIONS

Real Life Use #1 (No Repetition)How many ways can first and second place be awarded to 10 people?10!/(10-2)! = 10!/8! = 3,628,800/40,320 = 90

Real Life Use #2 (With repetition)How many permutations are there in a three digit lock with number options 0-9?10 × 10 × ... (3 times) = 10^3 = 1,000 permutations

Real Life Use #3If nine students take a test and all have different scores, the highest score could be achieved by any of the nine students. The second highest score could be achieved by one of the remaining 8 students. The third highest score could be achieved by one of the 7 remaining students.The number of possible permutations would be: P(9,3) = 9!/(9-3)! = 9*8*7 = 504 possible arrangements of the top three scores.

Sourceshttp://mathworld.wolfram.com/Permutation.htmlhttp://www.mathsisfun.com/combinatorics/combinations-permutations.htmlhttp://www.youtube.com/watch?v=tg__uC4pytkhttp://www.youtube.com/watch?v=n19HRkqCuUMhttp://www.aaamath.com/sta-permu.htm

ConclusionPermutations are ordered combinations. It is important to note that order does matter in these problems. Moreover, factorials are a key to the understanding of this topic. Permutations are divided in two types, with and without repetition. They both rely on the same formula, however, there is a shotcut for those with repetition. This was a challenging project since we had to learn these topics on our own.


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