How do I solve the following problem using factorials or permutations?The Super bowl Committee has applications from 9 towns to host the next two...

(a)  If the town cannot host a Super Bowl two consectutive
years, use the following permuation:

Use the permuation
nPk, which is the permutation of n events can form k sequences without
repetition.

nPk = n! / (n -
k)!

If the town cannot repeat a Super Bowl two consecutive
years, then...

n = 9 (the number of events, in this case,
the number of towns)

k = 2 (the number of sequences without
repetition)

9! / (9 - 2)!

9! /
7!

362,880 / 5,040 = 72

If the
town can host a Super Bowl two consecutive years, you do not use a permutation because a
permutation requires non-repetition.  Instead, use the multiplication counting
principle.

According to the multiplication counting
principle, if you have m ways to make the first choice and n ways to make the second
choice, then you have m*n ways to make both choices.

For
the first year, you have 9 choices of towns.  For the second year, you have 9 choices of
towns.  Therefore...

m = 9

n =
9

m * n = 9 * 9 =
81

Answers:

(a) 
72 ways

(b)  81
ways