How many 8-digit telephone numbers have one or more repeated digits?

Answer 1

Well, that depends on what rules you want to follow as far as formatting the number is concerned. Can the first digit be a zero? Can it be anything other than a 1?. That is, does it have to be a valid phone number?

Let's assume that the first digit can be anything. We can work the answer out as follows:

Total number of 8-digit numbers (with preceding 0's):

108

Total number of 8-digit numbers that have all unique digits:

10! / 2!

Therefore, the total number of 8-digit numbers - allowing preceding 0's - would be 108 - 10!/2! = 100000000 - 1814400 = 98185600

Now, if you don't want to allow a preceding zero, then your first digit can only be 1-9. So instead we get:

9 * 107 - 9 * (9! / 2!) = 90000000 - 1632960 = 88367040