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Math Help - General Combination Questions

  1. #1
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    General Combination Questions

    just some questions that i need help with, if someone could help, it would be appreciated very much

    q1. find the number of ways of arranging 7 people in a line with the tallest in the middle

    q2. a squad of footballers has 10 midfielders, 3 goalkeepers and 7 defenders. how many teams (of 11 players) could be selected if the team only has one goalkeeper and at least 5 midfielders and at least 4 defenders?
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  2. #2
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    Hello, gbooker!

    (1) Find the number of ways of arranging 7 people in a line
    with the tallest in the middle.

    Place the lallest in the middle.

    Then the other six people can be arranged in 6! = 720 ways.



    (2) A squad of footballers has 3 Goalkeepers, 10 Midfielders, and 7 Defenders.
    How many teams (of 11 players) could be selected if the team has:
    one Goalkeeper and at least 5 Midfielders and at least 4 Defenders?
    There are two possible team compositions:

    . . 1G,\;6M,\;4D\!:\;\;{3\choose1}{10\choose6}{7\choos  e4} \;=\;22,\!050 possible teams.

    . . 1G,\;5M,\;5D\!:\;\;{3\choose1}{10\choose5}{7\choos  e5} \;=\;15,\!876 possible teams.


    Therefore, there are: . 22,\!050 + 15,\!876\;=\;37,\!926 possible teams.

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  3. #3
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    thanks
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