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# Probability

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1. I'm stuck on this question:

Each of n people drops his business card into an urn. They each then choose a card at random from the urn. Write down a formula for the probability that none of the n people gets his own card.

The answer is but I'm not sure how.

Appreciate any help, thanks.
2. Its 50% - Either the N People get their own card or they dont.
3. (Original post by r3l3ntl3ss)
I'm stuck on this question:

Each of n people drops his business card into an urn. They each then choose a card at random from the urn. Write down a formula for the probability that none of the n people gets his own card.

The answer is but I'm not sure how.

Appreciate any help, thanks.
This is what is called a derangement. Probably the slickest way of doing this is via the inclusion exclusion formula. Do you know about that?
4. (Original post by Gregorius)
This is what is called a derangement. Probably the slickest way of doing this is via the inclusion exclusion formula. Do you know about that?
yep I know about the inclusion exclusion formula, but I'm unsure about how to begin
5. (Original post by r3l3ntl3ss)
yep I know about the inclusion exclusion formula, but I'm unsure about how to begin
Let be the event that person does get their card. You want . Now start crunching the formula.
6. (Original post by Gregorius)
Let be the event that person does get their card. You want . Now start crunching the formula.
ah I see, thank you!

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