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Math Help - Probability - need the answers to know if im on the right track while practicing

  1. #1
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    Probability - need the answers to know if im on the right track while practicing

    1. in how many ways can a hockey team consisting of 11 players be chosen from a squad of 14 players

    2. 80 disc marked with the numbers 1 to 80 are placed in a box and one disc is drawn from it. determine the probability that the number on the disc will be a multiple of 5

    3. A bag contain 4 red marbles, 3 blue marbles and 7 green marbles. A marble is drawn from the bag. What is the probability that it will be a red marble.

    4. In how many ways can one select a committee of four republicans, three democrats and two independents from a group of 10 distinct republicans, 12 distinct Democrats and 4 distinct independents?
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    Re: Probability - need the answers to know if im on the right track while practicing

    A better idea, show us what you have done (to prove you have shown some effort) and we will check over it..,
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    Re: Probability - need the answers to know if im on the right track while practicing

    Q1 sol
    n/r!(n-r)!

    14/11(14-11)

    14*13*12/3 = 728

    Q2 Not sure where to even sart

    Q3 sol

    4+3+7 = 14

    1/14

    Q4 sol

    10/4(10-4) * 12/3(12-3) * 4/2(4-2)

    10/4(6) * 12/3(9) * 4/2(2)

    5040/24 * 1320/6 * 12/2

    answer seem too big not sure if correct
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    Re: Probability - need the answers to know if im on the right track while practicing

    Q1: \dfrac{14!}{11!(14-11)!} = \dfrac{14\cdot 13\cdot 12}{3\cdot 2\cdot 1} = 364

    Q2: Every five numbers is a multiple of 5. Since 80 is divisible by 5, you have a \dfrac{1}{5} chance of drawing a multiple of 5. But, in general, you need to find out how many multiples of 5 are among the numbers 1 to 80 (there are \dfrac{80}{5} = 16). Then, the chances of drawing a multiple of 5 are \dfrac{16}{80} = \dfrac{1}{5}.

    Q3: Four of the fourteen marbles are red. So, you have a \dfrac{4}{14} = \dfrac{2}{7} chance of drawing a red marble.

    Q4: Use the exclamation mark for factorial.
    \dfrac{10!}{4!6!}\dfrac{12!}{3!9!}\dfrac{4!}{2!2!} = \dfrac{10\cdot 9\cdot 8\cdot 7}{4\cdot 3\cdot 2\cdot 1}\cdot \dfrac{12\cdot 11\cdot 10}{3\cdot 2\cdot 1}\cdot \dfrac{4\cdot 3}{2\cdot 1} = 277,200
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