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Math Help - Combinations #1

  1. #1
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    Combinations #1

    A class contains 10 boys and 15 girls. 8 can go to a local castle, 7 can go to the theatre and the remainning 10 will go to the museum.

    In how many ways can the class be divided for their activity day if the group going to the theatre must consist of 4 girls and 3 boys.

    thanks!
    Last edited by mr fantastic; December 9th 2009 at 05:53 PM. Reason: Changed post title
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  2. #2
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    Hello, BabyMilo!

    A class contains 10 boys and 15 girls.
    8 can go to a local castle, 7 can go to the theatre, the remainning 10 will go to the museum.

    In how many ways can the class be divided for their activity
    day if the group going to the theatre must consist of 4 girls and 3 boys?

    Choose 4 girls to go to the theatre: . {15\choose4} = 1365 ways.

    Choose 3 boys to go to the theatre: . {10\choose3} = 120 ways.

    The other 18 students are divided into a group of 8 and a group of 10.
    (Their genders do not matter.) .There are: . {18\choose8,10} = 43,\!758 ways.


    Therefore, there are: . 1365 \times 120 \times 43,\!758 \;=\;7,\!167,\!560,\!400 ways.

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, BabyMilo!


    Choose 4 girls to go to the theatre: . {15\choose4} = 1365 ways.

    Choose 3 boys to go to the theatre: . {10\choose3} = 120 ways.

    The other 18 students are divided into a group of 8 and a group of 10.
    (Their genders do not matter.) .There are: . {18\choose8,10} = 43,\!758 ways.


    Therefore, there are: . 1365 \times 120 \times 43,\!758 \;=\;7,\!167,\!560,\!400 ways.

    thanks for you reply but the answer in the back is 4 181 076 900
    but again this could be wrong.

    Can you check your answer and the answer in the back of the book.

    thanks!
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  4. #4
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    Quote Originally Posted by BabyMilo View Post
    thanks for you reply but the answer in the back is 4 181 076 900 but again this could be wrong.
    I also get 7167560400 as did Soroban.
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