Probability of matching n words with n pictures correctly

[BifSlamkovich]

Suppose there are n pictures and n words. Each word matches with exactly one out of the n pictures. What is the probability function of having exactly y words match up correctly?

 

[Simon Bridge]

Depends on how the words and pics getting sorted?
Write the words on cards, stack, shuffle, and deal them out between the pics?
The first card has a 1/n chance of being next to the right picture - but, if it is wrong, then another card is guaranteed to be next to a wrong picture. That will be your problem.

Anyway - this sort of thing is commonly described as seating dinner guests against their place-cards.

 

[BifSlamkovich]

Depends on how the words and pics getting sorted?
Write the words on cards, stack, shuffle, and deal them out between the pics?

Yes.

 

[moonman239]

Depends on how the words and pics getting sorted?
Write the words on cards, stack, shuffle, and deal them out between the pics?
The first card has a 1/n chance of being next to the right picture - but, if it is wrong, then another card is guaranteed to be next to a wrong picture. That will be your problem.

Anyway - this sort of thing is commonly described as seating dinner guests against their place-cards.

Do you know the solution? I can write one, but mine gets more complicated as n increases.]

Edit: Can you use the hypergeometric distribution to get the answer?

 

[awkward]

The answer is given by the "Rencontres numbers". See the entry labeled "Proabability distribution" on this page:

http://en.wikipedia.org/wiki/Rencontres_numbers