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# Let’s count – Derangements

Let's count - Derangements
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the complete solution of the exercises in the video or in the pdf below.

### Exercise 1.

In how many ways can one distribute 10 books to 10 children (one book to each one), and then collect the books and redistribute them in such a way that every children gets a new book?

### Exercise 2.

Consider the red cards (13 hearts and 13 diamonds) from a poker deck of 52 cards. The 13 heart cards are distributed to 13 people, and then the diamonds, with one card of each type to each person.

1. How many possible outcomes are there for such a distribution?

2. What is the probability that at least one person receives a pair (two cards with the same face value)?

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