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Math Help - (2) Probability Q's

  1. #1
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    (2) Probability Q's

    1.) In a club of 10 members...How many ways are there to choose a President, and an Advising Council of 3 members?

    2.) A deli offers ham sandwiches, roast beef sandwiches, cheese sandwiches, turkey sandwiches, and salami sandwiches. You are sent in to buy sandwiches for a group of ten people for lunch. How many different ways can you order lunch?

    3.) In a club of 10 members...How many ways are there to choose a President, a Vice President, a Secretary, and a Treasurer?

    I'm I correct w/ using nCr (n=10,r=4) .... which equals 210 different ways?
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  2. #2
    Senior Member Twig's Avatar
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    Yes,  \frac{10!}{4! \cdot (10-4)!} = 210

    For Q1, you can choose a president 10 ways, and then for each choice of president, your council will consist of three people from a group of nine.

     10 \cdot \frac{9!}{3! \cdot (9-3)!} = 840

    For Q2, I think the answe is (n+k-1)C(k) .
    Last edited by Twig; April 17th 2009 at 01:08 AM.
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  3. #3
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    Quote Originally Posted by toop View Post
    1.) In a club of 10 members...How many ways are there to choose a President, and an Advising Council of 3 members?

    2.) A deli offers ham sandwiches, roast beef sandwiches, cheese sandwiches, turkey sandwiches, and salami sandwiches. You are sent in to buy sandwiches for a group of ten people for lunch. How many different ways can you order lunch?

    3.) In a club of 10 members...How many ways are there to choose a President, a Vice President, a Secretary, and a Treasurer?

    I'm I correct w/ using nCr (n=10,r=4) .... which equals 210 different ways?
    2) You have 5 possible sandwich choices for each of the 10 people, so the number of possibilities is 5^{10}.
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  4. #4
    Senior Member Twig's Avatar
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    order irrelevant

    awkward, I donīt think that is what he meant. I think he meant that you go into the diner and need to buy 10 sandwiches. The order is irrelevant.
    Thatīs the way I interpreted the question.
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  5. #5
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    Quote Originally Posted by Twig View Post
    awkward, I donīt think that is what he meant. I think he meant that you go into the diner and need to buy 10 sandwiches. The order is irrelevant.
    Thatīs the way I interpreted the question.
    Hi Twig,

    That's a good point-- it depends on the interpretation of the question. To me it seems that the question of who gets which sandwich is relevant-- it would matter if it was my sandwich! But either interpretation is plausible.

    Awkward
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  6. #6
    Senior Member Twig's Avatar
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    Definetely
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