A pin has 4 different digits, how many pins

Step by step

The question

Question: A PIN has 4 different digits (0 to 9).

How many PINs are there?

1 Count the choices

2 Multiply

Every choice goes with every other choice.

So we multiply them all: 10 × 9 × 8 × 7.

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.

720 times 7 is 5040.

So there are 5040 PINs.

3 Check

Let's check in another order.

First 9 times 8 times 7 is 504.

Then 10 times 504 is 5040.

The same.

So the answer is right!

Let's look back.

First: count the choices.

Then: multiply.

Last: check.