# Field trip

• May 13th 2013, 09:58 AM
SummerTime
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
• May 14th 2013, 12:32 AM
chiro
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?