Six students (Dave, Michael, Ann, Joe, Jane, Bill) are attending a lecture in a classroom with 10 seats. The seats are in a single row as follows All valid seating arrangements are equally likely. By valid seating arrangement, we mean that all students have to sit down in a seat and students can not share seats. Here is an example of a valid seating arrangement:

Dave - B, Michael - A, Ann - E, Joe - I, Jane - H, Bill - F

(a) How many seating arrangements are there? Note that who sits where matters.

(b) What is the probability of the seating arrangement Dave - A, Michael - C, Ann - D, Joe - H, Jane - I, Bill - J?

(c) What is the probability that Dave sits in seat A?

(d) What is the probability that seats A, C, D, H, I and J are occupied?

(e) What is the probability that seat A is occupied?

(f) What is the probability that Dave sits in A and Michael sits in C or Dave sits in A and Bill sits in F?