How many five digit numbers have at least one digit that occurs more than once?

Select one:

1. 27,216
2. 967,125
3. 0
4. 62,784
5. 732

The answer is 62784 as shown, and that can be solved through:

[total amount of 5 digit numbers] - [5 digit numbers with completely unique/non-repeating digits] = [5 digit numbers with repeating digits]

See explanation for more detail and computations.

Step-by-step explanation

Since the total set of 5 digit numbers are made of those with unique digits, and those that are not (i.e. have repeating digits), we can just find the total minus those with unique digits.

To get the total amount of 5 digit numbers:

9*10*10*10*10 = 90000

Here, the highest place value can only have 9 possibilities because it cannot be 0, or else it will be a 4 digit number instead.

To get the amount of 5 digit numbers with no repeating digits:

9*9*8*7*6 = 27216

For the same reason as above, the 1st digit can only have 9 possibilities. The 2nd digit also has 9 possibilities because out of the 10 possible digits, 1 of them has already been used. The same pattern goes for the next digits, so -1 possibility as you go on.

So: 90000 - 27216 = 62784