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Math Help - Need help with this

  1. #1
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    Need help with this

    The question is as follows:

    You have 12 programs that need to be processed. How many ways can you order these 12 programs if

    a. there are no restrictions?
    b. you consider 4 programs higher in priority than the other 8 and want to process those 4 first?
    c. you seperate the programs into 4 of top priority, 5 of lesser priority, and 3 of least priority and you want to process them so the top priority is processed first and the 3 programs of least priority are processed last?

    So far this is what I have:
    a. 12!
    b. 12!/4!
    c. 12!/(4!5!3!)

    Can anyone please help me and let me know if this looks right or if I am doing anything wrong. thanks.
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  2. #2
    Senior Member
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    Quote Originally Posted by ashkash
    The question is as follows:

    You have 12 programs that need to be processed. How many ways can you order these 12 programs if

    a. there are no restrictions?
    b. you consider 4 programs higher in priority than the other 8 and want to process those 4 first?
    c. you seperate the programs into 4 of top priority, 5 of lesser priority, and 3 of least priority and you want to process them so the top priority is processed first and the 3 programs of least priority are processed last?

    So far this is what I have:
    a. 12!
    b. 12!/4!
    c. 12!/(4!5!3!)

    Can anyone please help me and let me know if this looks right or if I am doing anything wrong. thanks.
    I'd say (a) correct, (b) 4!8! and (c) 4!5!3!.

    For problems like this, it helps to try a smaller example to see if your formula works. Say it was 4=2+2 programs for (b). The number of ways to order them is

    1234
    1243
    2134
    2143

    which is 2!2!, but not 4!/2!.
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  3. #3
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    Lexington, MA (USA)
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    Hello, ashkash!

    You have 12 programs that need to be processed.
    How many ways can you order these 12 programs if

    a. there are no restrictions?

    You are correct . . . There are 12! orderings.


    b. you consider 4 programs higher in priority than the other 8
    and want to process those 4 first?

    There are 4! orderings for the four high-priority programs
    . . and 8! orderings for the remaining eight programs.

    Therefore, there are: (4!)(8!) possible orderings.



    c. you seperate the programs into 4 of top priority, 5 of lesser priority, and 3 of least priority
    and you want to process them so the top priority is processed first
    and the 3 programs of least priority are processed last?

    There are 4! orderings of the four top-priority programs,
    . . 5! orderings of the five lesser-priority programs,
    . . and 3! orderings of the three least-priority programs.

    Therefore, there are: (4!)(5!)(3!) possible orderings.

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  4. #4
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    got it, thanks for your help guys
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