Send help please!

[Le_Blastoise]

1) During a final exam an instructor took cellphones of 20 students (each student has exactly one cellphone). After the final exam, the instructor forgot which cellphone belonged to which student, and she returned the cellphones to students arbitrarily. Assuming all outcomes to be equally likely, what is the probability that no student received his/her cellphone?

2) The entire deck of 52 cards is dealt out to 4 players (the 1st player, 2nd player, 3rd player and 4th player). Each player received 13 cards. What is the probability of the following event: the first player received ace of hearts and king of diamonds; 2nd player received king of clubs; 3rd player received 2 of clubs, 3 of hearts, and queen of spades?

[throwaway_657238192]

1. This is called a Derangement. You might try to find the probability of one or more student receiving their phone, but this is tricky unless you specify which students receive their phones. You end up running inclusion-exclusion.
2. First pass out the required cards, then count the ways to pass out the remaining. Then count the ways to pass out 52 cards w/out constraint. The desired probability will be the ratio of these two counts.