A code has 3 different digits, how many codes

Step by step

The question

Question: A code has 3 different digits (0 to 9).

How many codes are there?

1 Count the choices

2 Multiply

Every choice goes with every other choice.

So we multiply them all: 10 × 9 × 8.

This is the counting principle: multiply the number of choices.

Careful!

We do not add the choices.

Every choice goes with every other one, so we multiply.

10 times 9 is 90.

90 times 8 is 720.

So there are 720 codes.

3 Check

Let's check in another order.

First 9 times 8 is 72.

Then 10 times 72 is 720.

The same.

So the answer is right!

Let's look back.

First: count the choices.

Then: multiply.

Last: check.