if there are 5 classes and each class have 30 students what is the probabity that if we select 2 students and that 2 students are from the same class?

Question

Kindly solve this problem. Thank you

Answer 1

Each class having the same number of students makes life easy.

Select the first person. Then, there are 29 people left in his class and 30 left in each of the other 4 classes, so the probability that the next person is from the same class is 29/(29 + 4*30) = 29/149

An alternate solution.

There are 5 classes, and C(30,2) pairs in each class.

There are C(150,2) total pairs.

Thus, P(both students are from same class) = 5 C(30,2)/C(150,2) = 5 * 30 * 29/2!/(150*149/2!) =

29/149