Alan is looking forward to return to in-person lectures! His four friends (Bob, Chris, Danny and Evelyn) and him enjoy sitting in the first row in the classroom. Assume that they each choose a seat at random in the first row and that there are 30 seats in the row. a) Calculate the number of ways that the five friends can sit in the first row. b) Calculate the probability that all five friends sit together as a group (all next to each other.) c) Calculate the probability that Alan will sit immediately next to his friend Bob. d) Calculate the probability that Alan and Danny will be separated by at least four seats between them. e) Calculate the probability that Alan will not be sitting immediately next to a friend.

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