Welcome to Mathnasium’s Math Tricks series. Whether it is in statistics or the real world, we are occasionally required to count large amounts. It can be a long and tedious process to list the total number of combinations for given events. So today we are showing you how to use the *Fundamental Counting Principle *to count the number of outcomes; the trick is to multiply the number of possibilities for each event together.

Use the Fundamental Counting Principle to find the number of combinations in the example below.

# Example: How many 3-digit numbers satisfy all of the following conditions?

**The first digit is greater than 6**.

**The second digit is an odd number**.

**The number is divisible by 2**.

** Step 1: Identify the possibilities for each condition.**

The first digit can be: 7, 8, 9.

The second digit can be: 1, 3, 5, 7, 9.

The 3-digit number must end in an even number to be divisible by two: 0, 2, 4, 6, 8.

** Step 2: Identify the number of possibilities for each condition.**

The first digit has 3 possibilities.

The second digit has 5 possibilities.

The third digit has 5 possibilities.

** Step 3: Multiply the number of possibilities for each condition.**

3 x 5 x 5 = 75

** Answer: 75**

Now, with the Fundamental Counting Principle, you are ready to solve counting problems. Click here for more practice problems, then check your answers here.

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