Question

A laptop lock has a 4 digit combination. Each character can be any digit between 0-7. The only restriction is that all 4 characters cannot be the same (e.g. 0000, 1111, 2222,... etc.). How many combinations are possible?

Answer 1

$4088$ are possible combinations .

Step-by-step explanation:

Here we have , A laptop lock has a 4 digit combination. Each character can be any digit between 0-7. The only restriction is that all 4 characters cannot be the same (e.g. 0000, 1111, 2222,... etc.). We need to find  How many combinations are possible .Let's find out:

The first digit has 8 choices (can be all of them), the second digit also has 8 choices. The third and fourth digits also have 8 choices.

Multiply them together you get:

⇒ $8(8)(8)(8)$

⇒ $4096$  possible combinations.

But since all 4 characters cannot be the same, we subtract 8 from 4096 (there are 8 combinations which the 4 characters are the same: 1111, 2222, 3333, 4444, 5555, 6666, 7777, and 0000) and we get :

⇒ $4096-8$

⇒ $4088$

Therefore, $4088$ are possible combinations .