Take the task of "building" 3-digit integers and break it into stages.

We’ll begin with the most restrictive stage.

Stage 1: Select a units digit
Since the integer must be odd, the units digit can be 1, 3, 7, or 9 (no 5's allowed)
So, we can complete stage 1 in 4 ways

Stage 2: Select a hundreds digit
This digit can be 1, 2, 3, 4, 6, 7, 8 or 9
So we can complete stage 2 in 8 ways

Stage 3: Select a tens digit
This digit can be 0, 1, 2, 3, 4, 6, 7, 8 or 9
So we can complete stage 3 in 9 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a 3-digit integer) in (4)(8)(9) ways (= 288 ways)

Answer: 288

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn

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