People on a plane!

(Motivated by snakes on a plane) Here are two of the standard people on plane problem just to get things rolling again:
1) There are (say) 100 seats on a plane and since people with disabilities board first, the blind person boards first. Let us say this isnt Southwest and that each person is assigned a fixed seat (even the blind person is assigned a seat) and if his seat is occupied, he will sit in any seat that is free. Let us further say that the blind person picks his seat randomly of all the ones on the plane. The question is: What is the probability that the last (100th) person gets to sit in his assigned seat?
2) (Easier) Say there are n seats and n people. What are the number of ways in which each person sits in a different seat?