Permutations

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by rsarahsm
Last updated 6 years ago

Discipline:
Math
Subject:
Prob/Stat

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Permutations

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A Permutation is an ordered Combination or group of items.

Permutations

Team1: Teresa O'Rourke, Julieta Garay, Maribel Silva, Christian Acosta

Albebra II, P.4

3 real life uses

Formula

In conclusion, I thought that this project was not efficient because of the meatod. I think that students learn better when taught by the teacher then by researching. Also some students only knew how to do the problems on their topic and did not know how to do other problems.

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These are the easiest to calculate.When you have n things to choose from ... you have n choices each time!When choosing r of them, the permutations are:n × n × ... (r times)(In other words, there are n possibilities for the first choice, THEN there are n possibilites for the second choice, and so on, multplying each time.)Which is easier to write down using an exponent of r:n × n × ... (r times) = nrExample: in the lock above, there are 10 numbers to choose from (0,1,..9) and you choose 3 of them:10 × 10 × ... (3 times) = 103 = 1,000 permutationsSo, the formula is simply:nrwhere n is the number of things to choose from, and you choose r of them(Repetition allowed, order matters)

In this case, you have to reduce the number of available choices each time. For example, what order could 16 pool balls be in?After choosing, say, number "14" you can't choose it again.So, your first choice would have 16 possibilites, and your next choice would then have 15 possibilities, then 14, 13, etc. And the total permutations would be:16 × 15 × 14 × 13 × ... = 20,922,789,888,000But maybe you don't want to choose them all, just 3 of them, so that would be only:16 × 15 × 14 = 3,360In other words, there are 3,360 different ways that 3 pool balls could be selected out of 16 balls.But how do we write that mathematically? Answer: we use the "factorial function" The factorial function (symbol: !) just means to multiply a series of descending natural

1! = 1Note: it is generally agreed that 0! = 1. It may seem funny that multiplying no numbers together gets you 1, but it helps simplify a lot of equations.So, if you wanted to select all of the billiard balls the permutations would be:16! = 20,922,789,888,000But if you wanted to select just 3, then you have to stop the multiplying after 14. How do you do that? There is a neat trick ... you divide by 13! ...16 × 15 × 14 × 13 × 12 ... = 16 × 15 × 14 = 3,36013 × 12 ...Do you see? 16! / 13! = 16 × 15 × 14The formula is written:where n is the number of things to choose from, and you choose r of them(No repetition, order matters)

No repetition

Repetition

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Lottery Ticket

Rubik's Cube

conclusion

Lock

Finding the permutation of AB means: how many different ways can you arrange the two letters like AB? (order matters)ABBAAs you can see, the only difference between our two permutations is the order. In our first one "AB," A is first and B is last. In the second one, "BA," all that we did was switch the order so that B goes first and A last.


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