MATH SOLVE

4 months ago

Q:
# A presidential candidate plans to begin her campaign by visiting the capitals in 44 of 5050 states. what is the probability that she selects the route of fourfour specific capitals? is it practical to list all of the different possible routes in order to select the one that is best?

Accepted Solution

A:

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."

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."