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

$^{50}P_4= \frac{50!}{(50-4)!} = \frac{50!}{46!} =50\times49\times48\times47=5,527,200$

Therefore, the probability that she selects the route of four specific​ capitals is $\frac{1}{5,527,200}$



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."