Part A:
Given that A
presidential candidate plans to begin her campaign by visiting the
capitals in 4 of 50 states.
The number of ways of selecting the route of 4 specific capitals is given by
[tex] ^{50}P_4= \frac{50!}{(50-4)!} = \frac{50!}{46!} =50\times49\times48\times47=5,527,200[/tex]
Therefore, the probability that she selects
the route of four specific capitals is [tex] \frac{1}{5,527,200} [/tex]
Part B:
The number of ways of selecting the route of 4 specific capitals is 5,527,200.
Since the number of ways of selecting the route of 4 specific capitals is too large it is not practical to list all of
the different possible routes in order to select the one that is best.
Therefore, "No, it is not practical to list all of the different possible
routes because the number of possible permutations is very
large."
