Car license plates consists of 7 digits. How many license plates can be made?

Question

shubhamsrg · Answer

You have to choose digits out of 10.
Can your combination of digits start with 0 ?

anonymous · Answer

No ,i think only from 1- 9.

shubhamsrg · Answer

0 is also a digit. And let us assume your combination does not start with 0.
Then choose 7 digits from 0-9. From this, subtract the possible combinations starting with 0.
Here we have also assumed digits do not repeat.

anonymous · Answer

Imagine a simple binary number. $$0000$$. Each digit can take the value of 1, or 0, meaning, you are limited to two numbers. How many combinations can we form with these two numbers (0 or 1), in 4 places? Well, it's $$2^4 = 2*2*2*2 = 16$$. 16 is the maximum number of combinations for a binary number of 4 places. You can take this concept and apply it to your problem, except this time, you have 9 numbers to choose from (1-9), and 7 places.

anonymous · Answer

Thank you guys so much, so it would be 8*8*8*8*8*8*8?

anonymous · Answer

Well, actually, if you have numbers 1-9, it would be $$9^7 = 9*9*9*9*9*9*9$$

anonymous · Answer

But as @shubhamsrg stated, 0 is a digit, so I imagine it will actually be $$10^7 = 10*10*10*10*10*10*10$$

anonymous · Answer

ahh alright i understand now! Thank you! :)