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

Hey guys ! Here's my problem : Sstudents in her class.

But due to budget constraints, the school is planning to take onlyNstudents for the trip. These students will be picked randomly.

And each student has equal chance of being picked.

Alice's friend circle hasMstudents including her.

Though she is excited about the field trip, she will enjoy it only if there are at leastKof 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