television programmer to assign commercial slots to a 30 min program subject to following rules:

-each commercial is one min long.

-there are no consecutive commercial slots

-the first min is not a commercial

-the 2nd minute is a commercial

-the last minute is a commercial

-there must be at least two minutes of non commercials between commercial slots.

a) if there are seven minutes of commercials in all, how many ways can the programer arrange them?

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pattern looks like this!

b) what if the network decides to have 8 commercial minutes (follow same restrictions)?