Question

A presidential candidate plans to begin her campaign by visiting the capitals in 44 of 4343 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

If the 4 states have to be in a specific order say ABCD, then the total number of different possible routes is:

 43P4 = 2,961,840

So the probability is:

1 / 2,961,840 = 3.38 x 10^-7

 

But if the 4 states can be in any order such as DBAC, ACBD etc, then the total number of different possible routes is:

 43C4 = 123,410

So the probability is:

1 / 123,410 = 8.1 x 10^-6

 

No I don’t think it is practical to list all the different possible routes to select the one that is best. We can simply use mathematical models to solve for that one.