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?

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

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- 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

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## 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: .$\displaystyle \frac{20}{120} \,=\,\frac{1}{6}$

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

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