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### Fixed-point-free permutations [duplicate]

An $i \in [n]$ is called a fixed point of a permutation $\sigma \in S_n$ if $\sigma(i) = i$. Let $D(n)$ be the amount of permutations $\sigma \in S_n$ without any fixed point. Prove that ...
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### Probability of matching events [duplicate]

Possible Duplicate: Number of permutations where n ≠ position n I have the following exercise: Suppose that four guests check their hats when they arrive at a restaurant, and that these hats are ...
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### Probability that no balls go in the right boxes [duplicate]

You have n balls, and n boxes. There is a pairing of each ball to a box (and vice versa). If you were to randomly place balls in boxes, what is the probability that none of the balls would go in "...
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### How many fix point free permutations of 5 elements are there? [duplicate]

I am trying to find out how many fix point free permutations of 5 elements there are. A permutation is fix point free, if $\pi (i) \neq i$. I am trying to solve this problem using the inclusion ...
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### The number of bijections $f$ of $\{1, 2,…, n\}$ such that $f(i) \ne i$ for any $i$ [duplicate]

Show that the number of bijections $f$ of $\{1, 2,..., n\}$ such that $f(i) \ne i$ for any $i$ is equal to $$\sum_{j=0}^{n}(-1)^j\frac{n!}{j!}.$$ Can I get some help for the above problem? I am not ...
Possible Duplicate: Number of permutations where n ≠ position n There are $N!$ permutations of the set $\{1,2,\ldots,N\}$ How many of them have zero identity elements? An identity element is an ...