A brand new standard deck of 52 playing cards comes with the cards arranged in a particular order. Before using them, the cards are shuffled. What is the probability that exactly 10 of the cards will remain in their original position?

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- December 7th 2009, 07:57 PMsbankicaderangement question
A brand new standard deck of 52 playing cards comes with the cards arranged in a particular order. Before using them, the cards are shuffled. What is the probability that exactly 10 of the cards will remain in their original position?

- December 7th 2009, 09:21 PMBruno J.
Clearly it's equal to the number of possible derangements of the remaining 42 cards, divided by . The number of derangements of objects is the integer closest to , in this case . So the probability is

. - December 8th 2009, 02:00 PMawkward
- December 8th 2009, 02:18 PMBruno J.
Oh yeah, where is my head! That'll teach me to try helping people at 2:00AM. (Giggle)