Hello Please help me on this question from Discrete Math. Fred is planning to go

Question

Hello Please help me on this question from Discrete Math.

Fred is planning to go to dinner each night of a certain week, Monday through Friday, with each dinner being at one of his ten favorite restaurants.

(a) How many possibilities are there for Fred’s schedule of dinners for that Monday through Friday, if Fred is not willing to eat at the same restaurant more than once?

(b) How many possibilities are there for Fred’s schedule of dinners for that Monday through Friday, if Fred is willing to eat at the same restaurant more than once, but is not willing to eat the same place twice in a row (or more)?

Explanation / Answer

a)

From Monday through Friday, without repeating any of the restaurants.Thus Monday will have 10 options to choose from, Tuesday 9 options, Wednesday 8 options and so on.

b)

From Monday through Friday, with repeatition of restaurants except on consecutive days.Thus Monday will have 10 options to choose from, Tuesday 9 options as repetitions are not allowed fro cosecutive days. Again on Wednesday 9 options as repetion is not allowed with the consecutive day Only. 9 options for Thursday and Friday as well.

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