### Brain Teasers

# Problems With the Windy City

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

In how many different ways can you rearrange the letters in the word "CHICAGO"?

### Hint

There are two C's in "CHICAGO".### Answer

At first glance, the response may seem to be simply 7!, or 5040. However, duplicates of the letter "C" poses a problem in the response. Any combination of letters, such as "ICCHOGA" can be created with C#1 coming first followed by C#2 or with C#2 preceding C#1. Any distinct possibility comes in pairs such as this. Therefore, to get rid of all duplicates, we divide 5040 (7!) in half to arrive at 2520, the answer to this problem.Hide Hint Show Hint Hide Answer Show Answer

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