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

Question

A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 48 states. What is the probability that she selects the route of three specific capitals? Is it practical to list all of the different possible routes in order to select the one that is best? A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 48 states. What is the probability that she selects the route of three specific capitals? Is it practical to list all of the different possible routes in order to select the one that is best? A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 48 states. What is the probability that she selects the route of three specific capitals? Is it practical to list all of the different possible routes in order to select the one that is best?

Explanation / Answer

  1/103776 if the three states have to be in a specified order say ABC or
1/17296 if they can be in any order ABC, ACB, BAC, BCA, CAB or CBA

Assuming the states are randomly chosen
If in EXACT order
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The first is 1 out of 48 = 1/48
The second is one out of 47 = 1/47 (one already visited first)
The third is one out of 46 = 1/46 (two already first and second)

Therefore the probability that she selects the route of three specified capitals AND in that one order
= 1/48 * 1/47 * 1/46 = 1/103776

In any order
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If she could go in ANY order however then it would be 3/48 * 2/47 * 1/46 = 6/103776 = 1/17296
ie the first state could be any of the three specified, the second state either of the two remaining that have been specified and the third whichever state specified had not been visited either first or second.


Therefore in conclusion 1/103776 if the three states have to be in a specified order OR
1/17296 if they can be in any order

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