Exercise 1.3

Question

Fred is planning to go out to dinner each night of a certain week, Monday through
Friday, with each dinner being at one of his ten favourite restaurants.
\begin{enumerate}[label=(\alph*)]
\item 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?
\item 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 at the same place twice in a row (or more)?
\end{enumerate}

fifthist x · Accepted Answer

\begin{enumerate}[label=(\alph*)]
\item Fred has $10$ choices for Monday, $9$ choices for Tuesday, $8$ choices 
for Wednesday, $7$ choices for Thursday and $6$ choices for Friday.

$$ 10 	imes 9 	imes 8 	imes 7 	imes6 $$

\item For the first restaurant, Fred has $10$ choices. For all subsequent days, 
Fred has $9$ choices since the only restriction is that he doesn't want to eat 
at the restaurant, he ate at the previous day.

$$ 10 	imes 9^{4} $$
\end{enumerate}

Exercise 1.3

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Exercise 1.3

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