Question

A lock on a fence door has a 4 digit combination. Each digit can be any number

between 0 – 9. The only restriction is that all 4 characters cannot be the same
(e.g. 1111, 2222, 3333, etc.). How many combinations are possible?




A. 504

B. 512

C. 10000

D. 9990

Answer 1

D. 9990 possible combinations

Explanation:

The first digit has 10 choices (can be all of them), the second digit also has 10 choices. The third and fourth digits also have 10 choices.

Multiply them together you get 10*10*10*10 = 10000 possible combinations.

But since all 4 characters cannot be the same, we subtract 10 from 10000 (there are 10 combinations which the 4 characters are the same: 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, and 0000) and we get 9990.

Answer 2

D. 9990 possible combinations

Explanation:

A lock on a fence door has a 4 digit combination. Each digit can be any number between 0 – 9. The only restriction is that all 4 characters cannot be the same (e.g. 1111, 2222, 3333, etc.). Therefore, there are 9990 possible combinations.