Question

A lock on a fence door has a 3 digit combination. Each digit can be any number between 1 – 8. The combinations 123, 456, and 789 are invalid. How many combinations are possible?

Answer 1

There are a total of 8 possible numbers for each digit and there are 3 digits for the password. Since the problem didn't state that the numbers can't be repeated, then we can apply the following formula:

`C_(n,m)\text{ = }\frac{n!}{m!(n\text{ - m)!}}`

Where "n" is the range of possibilities for each number and "m" is the number of digits we want to arrange them. So applying the data from the problem gives us: