1. ## hat problem

5 people go to a movie theathre. They consign their hats to a cloakroom. What is the probability that when they leaved the theathre 2 of them got their hats?

2. ## Re: hat problem

Originally Posted by kastamonu
5 people go to a movie theathre. They consign their hats to a cloakroom. What is the probability that when they leaved the theathre 2 of them got their hats?

3. ## Re: hat problem

Hello, kastamonu!

Five people go to a movie theatre and consign their hats to a cloakroom.
What is the probability that when they leave the theatre, exactly 2 of them got their hats?

Assuming that the hats are returned randomly,
. . there are $\displaystyle 5! = 120$ possible outcomes.

Call the people $\displaystyle A,B,C,D,E.$

First, choose the two people who get their hats.
. . There are: .$\displaystyle {5\choose2} = 10$ choices.

Suppose they are $\displaystyle A$ and $\displaystyle B.$
Then $\displaystyle C,D,E$ do not get their hats.
There are 2 choices: .$\displaystyle DEC$ and $\displaystyle ECD.$

Hence, there are: .$\displaystyle 10\cdot2 \,=\,20$ ways.

The probability is: .$\displaystyle \frac{20}{120} \,=\,\frac{1}{6}$

many thanks.