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

Step by step

The question

Question: A plate has 3 letters (A to Z) and then 2 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 × 26 × 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 26 is 17576.

17576 times 10 is 175760.

175760 times 10 is 1757600.

So there are 1757600 plates.

3 Check

Let's check in another order.

First 26 times 26 times 10 times 10 is 67600.

Then 26 times 67600 is 1757600.

The same.

So the answer is right!

Let's look back.

First: count the choices.

Then: multiply.

Last: check.