# Green, blue, red

**Discrete Mathematics**Level 3

Three 10-sided dice, each numbered 1 through 10, are rolled. One die is green, one die is blue, and one die is red. Kareem rolls the three dice and writes down the numbers showing on the green die, the blue die, and the red die, in that order. There are 1000 different ordered triples that Kareem could have written down. For how many of those triples is the number on the blue die strictly between the numbers on the red and green dice?

**Details and assumptions**

As an explicit example, the number 4 is strictly between the numbers 1 and 10.

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