Results 1 to 4 of 4

Thread: Probability

  1. #1
    wps
    wps is offline
    Newbie
    Joined
    Feb 2017
    From
    Earth
    Posts
    9
    Thanks
    2

    Probability

    A building has 10 doors and 5 persons will enter this building. What is the probability that the first four persons will enter the building through 4 different doors and the fifth person will use one of these 4 doors?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,536
    Thanks
    1701

    Re: Probability

    Hey wps.

    Can you show us what you have tried?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    wps
    wps is offline
    Newbie
    Joined
    Feb 2017
    From
    Earth
    Posts
    9
    Thanks
    2

    Re: Probability

    Choose 4 among 10 doors : P(10,4) ways
    All possibilities : 10^4
    Probability that the first 4 enter diff doors : \frac{P(10,4)}{10^4}
    Probability that the fifth person enter the same door : \frac{4}{10}
    Final answer : \frac{P(10,4)}{10^4} \times     \frac{4}{10}

    Is it correct?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,951
    Thanks
    2739

    Re: Probability

    Quote Originally Posted by wps View Post
    A building has 10 doors and 5 persons will enter this building. What is the probability that the first four persons will enter the building through 4 different doors and the fifth person will use one of these 4 doors?
    The first person can chooses any of the 10 doors. The second person can choose any of the 9 remaining doors, the third 8 doors and the fourth 7 doors. The fifth person enter through any of the those four doors. There are, then 10(9)(8)(7)(4) ways the five people can enter. Without any restrictions there are 10^5 ways for 5 people to enter through 10 doors. The probability of the given situation is \frac{10(9)(8)(7)(4)}{10^5}. Since _{10}P_4= \frac{10!}{(10- 4)!}= \frac{10!}{6!}= 10(9)(8)(7), that is the same as your answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 6th 2013, 10:29 AM
  2. Replies: 0
    Last Post: May 5th 2013, 07:32 PM
  3. Replies: 1
    Last Post: Jul 11th 2012, 05:42 AM
  4. Replies: 10
    Last Post: Jan 21st 2011, 11:47 AM
  5. Replies: 3
    Last Post: Dec 15th 2009, 06:30 AM

/mathhelpforum @mathhelpforum