# hat problem

• Mar 21st 2014, 12:34 PM
kastamonu
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?
• Mar 21st 2014, 12:52 PM
Plato
Re: hat problem
Quote:

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?

• Mar 21st 2014, 01:35 PM
Soroban
Re: hat problem
Hello, kastamonu!

Quote:

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 $5! = 120$ possible outcomes.

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

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

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

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

The probability is: . $\frac{20}{120} \,=\,\frac{1}{6}$
• Mar 22nd 2014, 01:23 AM
kastamonu
Re: hat problem
many thanks.