Suppose you are a math student and are recording the room number for all math students, one at a time until you have found a match (This means that a room number has already been recorded).

i) What is the probability that it takes more than 30 students for this to happen?

ii) What is the probability that is takes exactly 25 people for this to happen?

Suppose you are a math student and are recording the room number for all math students, one at a time you have found a student who shares the same dormitory room with you. What is the probability that it takes exactly 28 math students for this to happen?

Well, I think that for 1(i), I may first select 30 persons out of 400 students as the numerator, then all those 30 students have 400 choices, so the denominator would be 400^30.

As for 1(ii), I just did it in the same way as (i) but to change 30 into 25. I also multiply 25 since 1 out of 25 has the same choice.

As for 2, I think that everyone just make a different choice than me so i put (399/400)^28 as my answer.