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| Combinations and Permutations |
Combinations and Permutations
Let's say you have 9 people competing to place in the top three of a golf tournament. How many different possibilities are there for the top three in the tournament? Well, if we pick first place first, we have 9 people to choose from. After that, we would have 8 to choose from for second place, and 7 for third place. To calculate the total, we simply have to multiply them together:
9x8x7=505
This is an example of a permutation. A permutation is the number of different ordered possibilities that can occur in a given situation. A permutation can be with or without repetition, as can a combination. If we say that there is a permutation for n things with r possibilities, the formulae will be:
#####With Repetition: n^r
#####Without Repetition: n!/(n-r)!
Returning to the problem at the top, what if they were sitting in three identical chairs instead of having rankings? This is an example of a combination. In a combination, order doesn't matter. Therefore, every permutation of the same combination has to be eliminated. This creates two more formulae:
#####With Repetition: (r+n-1)!/(r!(n-1)!)
#####Without Repetition: n!/(r!(n-r)!)
###Sources “Combinations and Permutations.” Math is Fun, www.mathsisfun.com/combinatorics/combinations-permutations.html.
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