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Math Help - Somewhat straightforward multiplication principle/permutations question...help please

  1. #1
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    Somewhat straightforward multiplication principle/permutations question...help please

    Hi everyone, happy Tuesday.

    If you could please help me with this question I'd appreciate it.


    A zydeco band from louisiana will play 5 traditional and 3 original cajun compositions at a concert. in how many ways can they arrange the program if...

    1) they begin with a traditional piece?

    2) an original piece will be played last?

    thanks!


    so I'm not really sure where to begin... if they begin with a traditional piece is it just 5 x 4 x 3 x 2 x 1 ways times 3 x 2 x 1 ways? And same thing with number 2, except reversed?

    If you could show how you got the answer, that'd be much appreciated too. Thank you!!
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  2. #2
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    In order to get the right answer, you have to come up with a process of enumerating every possible program. So, first, think not about numbers but about choices. I agree, at first you choose one of the five traditional pieces. Then what? If you choose one of the four remaining traditional pieces, that would not cover every program because the initial piece may be followed by an original one.
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  3. #3
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    Thanks for you help! But I'm still stuck...if you could elaborate more, that'd be great. Do I draw a tree diagram?
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  4. #4
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    Quote Originally Posted by gobbajeezalus View Post
    Thanks for you help! But I'm still stuck...if you could elaborate more, that'd be great. Do I draw a tree diagram?
    The answer to the first is 5\cdot 7!.

    Try to explain why. Then post your try for the second one.
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  5. #5
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    After the first traditional piece you can play the rest 4 + 3 pieces in any order. It does not matter which of the remaining 7 pieces are traditional and which are original.

    Edit: Well, I complemented Plato to provide the complete solution.
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  6. #6
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    Oh, that makes perfect sense! After the 5 traditional pieces, the 4 traditional remaining and the 3 original have 7! orders PER original traditional piece so we multiply 5 x 7!

    20/20 hindsight, I guess...

    Now I'm still kind of lost on b.

    I'm trying to figure it out in a similar manner...

    this time we have the ! at the beginning, times 3 right?

    so whats the ! is it 5 + 3 -1 again, meaning 7! ?

    Thanks again!!
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  7. #7
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    Yes, it is 7! * 3.
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