What level is this course work?
The solution is quite intricate.
(I can't follow the given solution.)
Design an experiment of having two people drawing cards from two identical decks of cards each.
Define the event "match" if both people draw the same card during the same draw.
For example, both people drawing the during the 7th draw would be a match.
What is the probability of having a match after all N draws without replacement?
The first player's deck (deck ) can be any order.
Suppose the second player's deck (deck ) has no matches with deck .
Then deck is a derangement of deck ,
. . a permutation in which no cards match.
For , the probability of no matches is approximately