# Probability that 4 friends will be in the same class

A group of 60 second graders is to be randomly assigned to two classes of 30 each. Five of the second graders, Marcelle, Sarah, Michelle, Katy, and Camerin, are close friends.

(a) What is the probability that they will all be in the same class?

(b) What is the probability that exactly four of them will be in the same class?

(c) What is the probability that Marcelle will be in one class and her friends in the other?

What i tried

(a) Let's say there are two classes A and B, so this means all the five friends will be in class $A$, so this means the product of the probabilities of each girl being in class $A$. This gives $(1/2).(29/59).(28/58).(27/57).(26/56).(2)$.

(b)This means one of them is not in the same class, which means $(1/2).(29/59).(28/58).(27/57).(2)$

• You found the probability that they will all be in class A. You also need to find the probability they are all in class B. So the correct answer is double what you wrote. Aug 24, 2015 at 17:48
• For (b) any of the 5 can be the "loner" in any group. The rest have to be in the other group, so $5\cdot\frac{30}{59}\cdot\frac{29}{58}......$ Aug 24, 2015 at 18:12

You correctly calculated the probability that all 5 will be in class A. This is the same as the probability that all 5 will be in class B. All together, the probability that the 5 are in the same class is $$(29/59)\cdot (28/58) \cdot (27/57) \cdot (26/56)$$ You'll probably find it easier to find the answer to (c) first. You should end up with $$(30/59)\cdot(29/58)\cdot(28/57)\cdot (27/56)$$ You can get the answer to (b) by multiplying this answer by $5$.