Results 1 to 5 of 5

Thread: Combinations and Probability

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    3

    Question Combinations and Probability

    If my brother and I can invite 5 friends from a class of 15 to a party how many ways can we each pick 5 friends?

    What's the probability 6 different friends are invited?

    What's the prob my brother and I invite the same 5 people?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by mike View Post
    If my brother and I can invite 5 friends from a class of 15 to a party how many ways can we each pick 5 friends?

    What's the probability 6 different friends are invited?

    What's the prob my brother and I invite the same 5 people?
    Well, since this question's gone unanswered for a while, I'll stick my neck out here ....


    (a) $\displaystyle {15 \choose 5} \times {15 \choose 5}$.

    The reasoning: Each brother can choose 5 friends from 15 in $\displaystyle {15 \choose 5}$ ways. So the number of ways two brothers can choose is $\displaystyle {15 \choose 5} \times {15 \choose 5}$.


    (b) $\displaystyle \frac{ {15 \choose 5} \times {5 \choose 4} \times {10 \choose 1}}{ {15 \choose 5} \times {15 \choose 5}} = \frac{{5 \choose 4} \times {10 \choose 1} }{{15 \choose 5}} = \frac{50}{ {15 \choose 5}} = .....$.

    The reasoning:

    numerator = number of ways the two brothers can choose 6 different friends: one brother chooses 5 friends from the 15, then the other brother chooses 4 friends from that 5 and 1 friend from the remaining 10.

    denominator = number of ways the two brothers can choose 5 friends each = answer from part (a).


    (c) $\displaystyle \frac{ {15 \choose 5} }{{15 \choose 5} \times {15 \choose 5}} = \frac{1}{{15 \choose 5}}$.


    But since arrangements under restriction aren't my forte, you should probably wait for confirmation or refutation ......
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2008
    Posts
    3

    Just to check my answer...

    Is 15 C 5 = 3003?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    9
    Quote Originally Posted by mike View Post
    Is 15 C 5 = 3003?
    Yes.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, mike!

    I totally agree with mr F . . .


    If my brother and I can invite 5 friends from a class of 15 to a party,
    how many ways can we each pick 5 friends?
    You have $\displaystyle {15\choose5}$ ways of picking 5 friends.
    Your brother has $\displaystyle {15\choose5}$ ways of picking 5 friends.
    . . Therefore, the two of you have: .$\displaystyle {15\choose5} \times {15\choose5} \;=\;3003^2$ ways.




    What's the probability 6 different friends are invited?
    You can pick any group of 5 friends . . . it doesn't matter.

    Your brother must pick 4 of your 5 choices: .$\displaystyle {5\choose4} \:=\:5$ ways.
    . . And he must pick one of the other ten friends: .$\displaystyle {10\choose1} \:=\:10$ ways.
    . . Hence, he has $\displaystyle 5\times 10 \:=\:50$ ways to add a sixth friend.

    Therefore, the probability is: .$\displaystyle \frac{50}{{15\choose5}} \;=\;\frac{50}{3003}$




    What's the prob my brother and I invite the same 5 people?

    You can pick any group of 5 friends . . . it doesn't matter.

    Your brother must pick the same 5 friends: .$\displaystyle 1$ way.

    Therefore, the probability is: .$\displaystyle \frac{1}{{15\choose5}} \;=\;\frac{1}{3003}$

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combinations and Probability
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: Apr 4th 2010, 11:28 PM
  2. Combinations and a bit of probability
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Dec 5th 2009, 12:11 PM
  3. Probability with combinations
    Posted in the Statistics Forum
    Replies: 6
    Last Post: Dec 5th 2009, 06:38 AM
  4. Combinations and Probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Dec 1st 2008, 06:58 PM
  5. Probability and Combinations
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Nov 12th 2008, 05:24 PM

Search Tags


/mathhelpforum @mathhelpforum