Have you ever wondered how many possible codes there are for a 4 digit lock? The answer may surprise you – there are a staggering 10,000 possible combinations! In this article, we’ll look at the mathematics behind this impressive figure.

## How Many Possible Codes Are There For a 4 Digit Lock?

A 4-digit code is made up of four numbers, each of which can be between 0-9. This means that for the first number you have 10 possible combinations (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). For the second number, you also have 10 possible combinations as the numbers can’t repeat. This means that for the first two numbers, you have 100 possible combinations (10 x 10).

For the third number, you have nine possible combinations as you can’t use the same number as the first or second. For the fourth number, you have eight possible combinations as you can’t use the same number as the first, second or third. This means that for the last two numbers, you have 72 possible combinations (9 x 8).

When you multiply the number of possible combinations for the first two numbers by the number of possible combinations for the last two numbers, you get 7,200 (100 x 72). However, this isn’t the full answer as the order of the numbers is also important. To calculate the total number of possible combinations, you have to multiply the number of possible combinations for the first two numbers by the number of possible combinations for the last two numbers, and then multiply this number by four.

This is because when you arrange the numbers, the order changes and there are four possible orders (for example, 1234, 2341, 3412, 4123). When you multiply 7,200 by 4, you get the answer of 28,800.

Finally, you have to take into account the fact that when you use the same number more than once, the number of possible combinations decreases. For example, if you were to use the number 1 more than once, the number of possible combinations would be reduced to 2,880 (7,200 divided by 4).

When you take all of these factors into account, the answer to the question ‘How many possible codes are there for a 4 digit lock?’ is 10,000 possible combinations. This impressive figure shows just how secure 4-digit locks can be.