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?

Results 1 to 4 of 4

- Mar 21st 2014, 11:34 AM #1

- Joined
- Oct 2012
- From
- Istanbul
- Posts
- 670
- Thanks
- 4

- Mar 21st 2014, 11:52 AM #2
## Re: hat problem

Read the article.

your answer is {5 choose 2}*{derangement of three}

- Mar 21st 2014, 12:35 PM #3

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 12,028
- Thanks
- 847

## 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 possible outcomes.

Call the people

First, choose the two people who get their hats.

. . There are: . choices.

Suppose they are and

Then do not get their hats.

There are 2 choices: . and

Hence, there are: . ways.

The probability is: .

- Mar 22nd 2014, 12:23 AM #4

- Joined
- Oct 2012
- From
- Istanbul
- Posts
- 670
- Thanks
- 4