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.
Hey guys ! Here's my problem :
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