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Math Help - [SOLVED] 33b-counting problem-players and line up

  1. #1
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    Red face [SOLVED] 33b-counting problem-players and line up

    I don't understand how to do this or which formulas to use.

    A little league team has 15 players.
    How many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters?
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  2. #2
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    possible solution. please check.

    Quote Originally Posted by yvonnehr View Post
    I don't understand how to do this or which formulas to use.

    A little league team has 15 players.
    How many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters?
    Well, I think the book's answer may be wrong on this one. Here is my solution. Is this correct?

    (15 choose 9) x 9! = 181681894400

    "15 choose 9" represents the number of ways you can pick 9 players from the 15 on the roster, and 9! represents the possible ordered lineups. I multiplied them together because because we are matching one set of outcomes to the other set of outcomes.
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  3. #3
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    Hi yvonnehr!

    Quote Originally Posted by yvonnehr View Post
    I don't understand how to do this or which formulas to use.

    A little league team has 15 players.
    How many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters?
    To select 9 players out of 15 there are \begin{pmatrix} 15\\ 9 \end{pmatrix} different ways.

    After that there are 9 players and nine different positions (1,2,3,4...,8,9).
    There are 9! ways tochoose the batting order.

    So the solution of this problem is

    \begin{pmatrix} 15 \\ 9 \end{pmatrix}*9!

    regards
    Rapha

    Edit:

    Quote Originally Posted by yvonnehr View Post
    Well, I think the book's answer may be wrong on this one. Here is my solution. Is this correct?

    (15 choose 9) x 9! = 181681894400

    "15 choose 9" represents the number of ways you can pick 9 players from the 15 on the roster, and 9! represents the possible ordered lineups. I multiplied them together because because we are matching one set of outcomes to the other set of outcomes.
    Yes, that sounds good.
    By the way what is the book's answer?
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  4. #4
    Member garymarkhov's Avatar
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    Quote Originally Posted by yvonnehr View Post
    A little league team has 15 players. How many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters?
    Are there two questions here? If you start by selecting 9 players for the starting lineup and don't care about their batting order, there are 15!/(6!*9!) = 5005 combinations. Then, once you start caring about batting order, there are 15!/6! = 1816214400 permutations.

    By the way, I used to get confused by combinations and permutations all the time. No more after reading Easy Permutations and Combinations | BetterExplained
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