Question

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?

Answer 1

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


`^(50)P_4= (50!)/((50-4)!) = (50!)/(46!) =50*49*48*47=5,527,200`

Therefore, the probability that she selects the route of four specific​ capitals is
`(1)/(5,527,200)`



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."