Question

A presidential candidate plans to begin her campaign by visiting the capitals of 5 of the 50 states. If the five capitals are randomly selected without replacement, what is the probability that the route is Sacramento, Albany, Juneau, Hartford, and Bismarck, in that order?

Answer 1

0.000000003933

Explanation:

As the candidate will visit the capitals of 5 of the 50 states, the probability of each capital being selected is 1/50.

As we want a probability of 5 specific capitals in a specific order, we can calculate the probability of each capital being chosed:

First city being Sacramento: Probability of 1/50

Second city being Albany: Probability of 1/49 (as the first city is not available now)

Third city being Juneau: Probability of 1/48

Fourth city being Hartford: Probability of 1/47

Fifth city being Bismarck: Probability of 1/46

So the final probability is 1/(50*49*48*47*46) = 0.000000003933

Answer 2

The probability is 1/254,251,200

Explanation:

We proceed as follows;

Firstly, we are selecting 5 state capitals out of 50. The number of ways we can do this is 50P5 = 50!/5!(50-5)! = 254,251,200 ways

Now, out of this number of ways , only one route is desired in that particular order.

This means the probability of having the route scheduled in that particular order would be;

1/254,251,200