How many different ID cards can be made if there are three digits on a car in no digit can be used more than once? What if digits can be repeated?

Question

asked Dec 14, 2023 20.1k views

1 Answer

Ivica Pesovski · Answer 1 · 2023-12-20T00:25:00+0000

Step-by-step explanation

The question wants us to determine the number of different ID cards that can be made if there are 3 digits on a car.

To do so, let us first list out all the possible outcomes. These are:

We can see that there are 10 possible digits

For the first case where no digit can be used more than once, we will have

Therefore, there are

$10*9*8=720\text{ ID cards}$

For the second case, if the digits can be repeated, then, we will have

Then, since the numbers can be repeated, we will have

$10*10*10=1000\text{ ID cards}$