How many five-digit codes are possible if the first digit cannot be 0 and repetition of digits is allowed?

The condition for the five-digit code is that the first digit cannot be 0, which means the first digit can be any digit from 1 to 9. Since there are 9 possible choices for the first digit, we have 9 options for that place.

For the remaining four digits (second, third, fourth, and fifth), each can be any digit from 0 to 9 since repetition is allowed. Hence, for each of these positions, there are 10 options (0-9).

Now we can calculate the total number of possible five-digit codes by multiplying the number of choices for each position:

The first position: 9 options (1-9) The second position: 10 options (0-9) The third position: 10 options (0-9) The fourth position: 10 options (0-9) The fifth position: 10 options (0-9)

To find the total number of combinations, we multiply the number of possibilities for each position:

9 (first digit) × 10 (second digit) × 10 (third digit) × 10 (fourth digit) × 10 (fifth digit) = 9 × 10^4

Therefore, there are 90,000 possible five-digit codes under the given conditions.