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Eight people are attending a seminar in a room with eight chairs. In the middle of the seminar, there is a break and everyone leaves the room.
a) In how many ways can the group sit down after the break so that no-one is in the same chair as before?
b) In how many ways can the group sit down after the break so that exactly four people are in the same chair as before?
c) In how many way can the group sit down after the break so that at least four people are in the same chair as before?
Note that your answer in each case should be an integer.
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