A plate has 2 letters and 3 digits, how many plates

Step by step

The question

Question: A plate has 2 letters (A to Z) and then 3 digits (0 to 9).

How many plates are there?

1 Count the choices

2 Multiply

Every choice goes with every other choice.

So we multiply them all: 26 × 26 × 10 × 10 × 10.

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.

26 times 26 is 676.

676 times 10 is 6760.

6760 times 10 is 67600.

67600 times 10 is 676000.

So there are 676000 plates.

3 Check

Let's check in another order.

First 26 times 10 times 10 times 10 is 26000.

Then 26 times 26000 is 676000.

The same.

So the answer is right!

Let's look back.

First: count the choices.

Then: multiply.

Last: check.