### Instruction: All 50 states as well as the District of Columbia and Puerto Rico, have distinct two-letter postal abbreviations. If a two-letter sequence of letters (such as CO or EE) is chosen at random, what is the probability that it is a postal abbreviation for one of the 50 states, the District of Columbia, or Puerto Rico? Express your answer as a common fraction.### Response: I need to find the total number of possible two-letter sequences and the number of those that are postal abbreviations for the given regions.
For the total number, I can use the multiplication principle: there are 26 choices for the first letter and 26 choices for the second letter, so there are 26 x 26 = 676 possible sequences.
For the number of postal abbreviations, I can use the addition principle: there are 50 states, one district, and one commonwealth, so there are 50 + 1 + 1 = 52 postal abbreviations.
Therefore, the probability of choosing a postal abbreviation at random is 52/676, which I can simplify by dividing both the numerator and the denominator by 4.
The simplified fraction is 13/169.