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Thread: Permutations and Combinations Marathon

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    Permutations and Combinations Marathon

    To start off:
    The ratio of numbers of arrangements of (2n+2) different objects taken n at a time to the number of arrangements of 2n different objects n at a time is 14:5. Find the value of n.
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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by Rathin View Post
    To start off:
    The ratio of numbers of arrangements of (2n+2) different objects taken n at a time to the number of arrangements of 2n different objects n at a time is 14:5. Find the value of n.
    (2n+2)Cn / 2nCn = 14/5
    (2n+2)!/n!(2n+2-n)! * n!(2n-n)!/(2n)! = 14/5
    (2n+2)!/n!(n+2)! * (n!)^2 / (2n)! = 14/5
    (2n+2)(2n+1)/(n+2)(n+1) = 14/5
    5(2n+2)(2n+1) = 14(n+2)(n+1)
    5(4n^2 + 6n + 2) = 14(n^2 + 3n + 2)
    20n^2 + 30n + 10 = 14n^2 + 42n + 28
    6n^2 - 12n - 18 = 0
    n^2 - 2n - 3 = 0
    (n-3)(n+1) = 0
    n = -1, 3 but n>0
    n = 3

    EDIT: It's meant to be perms not combs but still gives the same answer as dividing those 2 combinations gets rid of the n! which is the difference between the P and C.
    Last edited by pikachu975; 23 Jul 2017 at 10:27 PM.
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    Re: Permutations and Combinations Marathon

    In how many ways can 5 writers and 5 artists be arranged in a circle so that two particular artists must not sit next to a particular writer. Note: The writers and artists sit alternately.
    Last edited by Green Yoda; 24 Jul 2017 at 8:42 PM.
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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by Rathin View Post
    In how many ways can 5 writers and 5 artists be arranged in a circle so that two particular artists must not sit next to a particular writer. Note: The writers and artists sit alternately.
    4!*5! = 2880

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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by bujolover View Post
    4!*5! = 2880
    That is for when the artists are seated alternatively only. However there are other conditions to the question.
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    Re: Permutations and Combinations Marathon

    Fix the writer = 1
    Sit 2 artists next to him = 3 x 2
    Sit the rest of the writers = 4!
    Sit the rest of the artists = 3!

    Multiply to get 864
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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by pikachu975 View Post
    Fix the writer = 1
    Sit 2 artists next to him = 3 x 2
    Sit the rest of the writers = 4!
    Sit the rest of the artists = 3!

    Multiply to get 864
    Yup that is correct!
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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by kawaiipotato View Post
    From the HSC 2017 MX2 Marathon thread.

    (I don't have the answer unfortunately.)
    Sxc avatar made by a sxc person: carrotontheground http://community.boredofstudies.org/...otontheground/

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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by kawaiipotato View Post
    From the HSC 2017 MX2 Marathon thread.

    (I don't have the answer unfortunately.)
    I dunno if its this simple tbh but:
    28C25 = 3276 ways
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    Re: Permutations and Combinations Marathon

    How many ways can eight basketball players be divided into four groups of two?
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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by Rathin View Post
    How many ways can eight basketball players be divided into four groups of two?
    8C2 x 6C2 x 4C2 x 2C2 / 4! = 28x15x6 / 4! = 105

    Divided by 4! because if you pick the same teams but arrange them in different order then it will give 4! arrangements, so you gotta get rid of those as if it's a repetition when arranging EEEE etc.
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    Re: Permutations and Combinations Marathon

    A 3-player game is played between Andy, Ben and Chuck.
    The probabilities that each of those players win a game are 0.5, 0.3 and 0.2 respectively.
    There are no drawn games.
    The winner of a tournament is the first player to win 6 games.
    The current score in the tournament (ie. games won) is:
    Andy - 3
    Ben - 4
    Chuck - 2
    To 5 decimal places, what is the probability that Andy wins the tournament from here?

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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by braintic View Post
    A 3-player game is played between Andy, Ben and Chuck.
    The probabilities that each of those players win a game are 0.5, 0.3 and 0.2 respectively.
    There are no drawn games.
    The winner of a tournament is the first player to win 6 games.
    The current score in the tournament (ie. games won) is:
    Andy - 3
    Ben - 4
    Chuck - 2
    To 5 decimal places, what is the probability that Andy wins the tournament from here?
    Most likely completely wrong but is the answer 0.18075
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    Re: Permutations and Combinations Marathon

    Quote Originally Posted by pikachu975 View Post
    Most likely completely wrong but is the answer 0.18075
    Sorry, I forgot I asked this question, and I can't find my solution. I just tried it again and got 0.31275.

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