SOLUTION: i need help learning factorials permutations

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Question 156465This question is from textbook algebra2
: i need help learning factorials permutations This question is from textbook algebra2

Answer by Electrified_Levi(103) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, Hope I can help
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I need help learning factorials permutations
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Factorials are given by the sign !
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(examples of factorials, 8!, 6!, 12!, 4! )
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Factorials use multiplication, (examples, 8! = +8%287%29%286%29%285%29%284%29%283%29%282%29%281%29+, 5! = +5%284%29%283%29%282%29%281%29+ )(whatever the number, you multiply that number by the numbers before it,(until you get to "1")
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45! = (45)(44)(43)(42)(41)(40)(39)(38) ... (25)(24)(23)(22) ... (6)(5)(4)(3)(2)(1), ( you multiply 45 by the numbers before it
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numbers (1 - 44))
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0! always equals "1", +0%21+=+1+
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Permutation is "how many ways can several things be arranged"
Now lets look at the permutation formula, Permutation formula = +n%21%2F%28n-r%29%21+
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"n" = total choices, "r" = how many are taken at a time
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It would be written as P(n,r), It is read as, Permutation, "n" things taken "r" at a time
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Lets do some examples,
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P(5,5), It is saying, "How many ways can 5 things be arranged if they are taken 5 at a time
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Since, P(n,r), we are trying to find, P(5,5), just replace "n" with "5", "r" with "5" in our equation
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+n%21%2F%28n-r%29%21+ = +%285%29%21%2F%28%285%29-%285%29%29%21+ = +%285%29%21%2F%280%29%21+ = +5%21%2F0%21+
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Now just multiply(remember, multiply that number by the numbers before it, until you hit "1")(remember that 0! = 1)
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+5%21%2F0%21+ = +%285%284%29%283%29%282%29%281%29%29%2F1+ = +%285%284%29%283%29%282%29%281%29%29%2F1+ = +120%2F1+ = +120+
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Let's do another one
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How many different ways can 10 different color paint cans, be arranged if they are taken 4 at a time
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Since "n" = total number of choices, "r" = how many things taken at a time
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It would be put like , P(n,r),P(10,4), replace "n" and "r" with (10)(n) and (4)(r) in equation
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+n%21%2F%28n-r%29%21+ = +%2810%29%21%2F%28%2810%29-%284%29%29%21+ = +%2810%29%21%2F%286%29%21+ = +10%21%2F6%21+
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If we expand the factorials, we get +10%21%2F6%21+ = = +3628800%2F720+ = +5040+
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The paint cans can be put in 5,040 different ways
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This formula is used only if the "objects are all different", there is another formula for "some objects that are the same", but I won't go into that, because you probably aren't doing that yet( if you need any more help just send another problem, and I will help answer the question)
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Hope I helped, Levi