How many five-digit codes can be made if the first number cannot be a 0 or a 1 and no numbers can repeat?

24,192.

Step-by-step explanation:

The first number must be one of 2,3,4,5,6,7,8 or 9. That is 8 possibilities.

The number of permutations of the other 4 numbers is 9P4

= 9! / (9-4) !

= 3024

Now we multiply by the 8:

3024 * 8

= 24,192.