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jmc

counting and probability senior

Problem

John has 12 marbles of different colors, including one red, one green, and one blue marble. In how many ways can he choose 4 marbles, if exactly one of the chosen marbles is red, green, or blue?
Solution
There are 3 ways for John to decide which of the red, green, and blue marbles to choose. After he has chosen one of them, he must choose 3 marbles from the other 9. There are ways for him to do this. The total number of valid ways for John to choose four marbles is .
Final answer
252