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Math Help - Field trip

  1. #1
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    Field trip

    Hey guys ! Here's my problem :
    Alice's school is planning to take some students from her class on a field trip. Alice is really excited about it. There are a total of S students in her class.
    But due to budget constraints, the school is planning to take only N students for the trip. These students will be picked randomly.
    And each student has equal chance of being picked.

    Alice's friend circle has M students including her.
    Though she is excited about the field trip, she will enjoy it only if there are at least K of her friends with her on the trip.
    What is the probability that she will enjoy her trip given that she goes on the trip?

    I know that if S = N then the probability will be 100% (all students are going)
    And if N = K (the number of students going is the same as the number of Alice's friends she wants to go with her) then the probability will be 0%.

    now in order to calculate the probability P i'm thinking about using a combination formula. How should i implement it ?

    Thank you very much
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  2. #2
    MHF Contributor
    Joined
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    Re: Field trip

    Hey SummerTime.

    What distributional assumptions are you using for the overall distribution: (Hint: You might want to consider looking at a hypergeometric distribution or its multivariable variety).

    Also are you just learning combinations or permutations or are you learning probability with distributions?
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