document.write( "Question 156465This question is from textbook algebra2
\n" ); document.write( ": i need help learning factorials permutations \n" ); document.write( "
Algebra.Com's Answer #115409 by Electrified_Levi(103)\"\" \"About 
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Hi, Hope I can help
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\n" ); document.write( "I need help learning factorials permutations
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\n" ); document.write( "Factorials are given by the sign !
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\n" ); document.write( "(examples of factorials, 8!, 6!, 12!, 4! )
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\n" ); document.write( "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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\n" ); document.write( "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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\n" ); document.write( "numbers (1 - 44))
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\n" ); document.write( "0! always equals \"1\", \"+0%21+=+1+\"
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\n" ); document.write( "Permutation is \"how many ways can several things be arranged\"
\n" ); document.write( "Now lets look at the permutation formula, Permutation formula = \"+n%21%2F%28n-r%29%21+\"
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\n" ); document.write( "\"n\" = total choices, \"r\" = how many are taken at a time
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\n" ); document.write( "It would be written as P(n,r), It is read as, Permutation, \"n\" things taken \"r\" at a time
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\n" ); document.write( "Lets do some examples,
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\n" ); document.write( "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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\n" ); document.write( "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" ); document.write( "\"+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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\n" ); document.write( "Now just multiply(remember, multiply that number by the numbers before it, until you hit \"1\")(remember that 0! = 1)
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\n" ); document.write( "\"+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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\n" ); document.write( "Let's do another one
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\n" ); document.write( "How many different ways can 10 different color paint cans, be arranged if they are taken 4 at a time
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\n" ); document.write( "Since \"n\" = total number of choices, \"r\" = how many things taken at a time
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\n" ); document.write( "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" ); document.write( "\"+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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\n" ); document.write( "If we expand the factorials, we get \"+10%21%2F6%21+\" = = \"+3628800%2F720+\" = \"+5040+\"
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\n" ); document.write( "The paint cans can be put in 5,040 different ways
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\n" ); document.write( "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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\n" ); document.write( "Hope I helped, Levi \n" ); document.write( "
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