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counting and probability intermediate

Problem

How many different four-letter arrangements can be formed using the six letters and , if the first letter must be , one of the other letters must be , and no letter can be used more than once in the arrangement?
Solution
There is 1 way to make the first letter C and 3 ways to make one of the other letters B. We now have 4 ways to pick the letter for the first remaining spot and 3 ways to pick the letter for the last remaining spot. This is a total of ways to arrange the letters.
Final answer
36