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 $(1/2).(29/59).(28/58).(27/57).(2)$
Best Answer
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 $5$.