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Math Help - permutations question #2

  1. #1
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    permutations question #2

    I thought I had this question solved and I sort of did bu I got only half of the answer.
    Solve ....
    6Pn=720

    so what I did was

    6!/(6-n)!=720
    6!/720=(6-n)! ****Also why cant you cancel the ! here, I mean why cant you divide it out here?
    6x5x4x3x2x1/720=6-n
    720/720=6-n
    n=6-1
    n=5

    but the answer that is given is 5 or 6? where is this 6 coming from?
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  2. #2
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    You can't divide it out there because the factorial is an operation, not a variable. You got to \frac{6!}{720}=(6-n)!, and then found that 6!=720, right? So then (6-n)!=1. You got the case for 1!=1, so that n=5 is a solution, as (6-5)!=1!=1. But there is another solution, as you noted. Here is a hint: what is 0! ("zero factorial")?

    --Kevin C.
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  3. #3
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    0!=1 but I dont see how that is applied to this question, and if its an operation not a variable why can you cancel it later.
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  4. #4
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    and what I mean by canceling later is my teacher said to do this

    example

    10Pn=90
    10!/(10-n)!=90
    10!=90(10-n)! *****I want to know why you cant cancel here.
    10!/90=(10-n)!
    8!=(10-n)!****but you can cancel here
    8=10-n
    n=2

    but if you canceled at 10!=90(10-n)! you have n= -.888888

    I dont see why my first example has 2 solutions and my second has one.
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  5. #5
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    Because you had (6-n)!=1. 1!=1, and as you noted, 0!=1, which means that 6-n can be 1 or 0, and thus n=5 or 6.

    --Kevin C.
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  6. #6
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    Quote Originally Posted by TwistedOne151 View Post
    Because you had (6-n)!=1. 1!=1, and as you noted, 0!=1, which means that 6-n can be 1 or 0, and thus n=5 or 6.

    --Kevin C.
    ya thanks I thought about it and also 7*6*5*4*3*2 when you cancel is =1!, =7*6*5*2*1 when you cancel its = 0! then when you cancel the factorials your left with 1/0. thanks.
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