Question

A student is given an ID number when they join a school district, such as GISD. The ID numbers consist of 6 digits, and the numbers range from 0 to 9. Any of the digits can be repeated, but 0 cannot be placed as the first digit. How many possible ID numbers are there?

a) 5,040
b) 531,440
c) 590,490
d) 531,441

Answer 1

The number of possible ID numbers can be calculated using permutations with repetition. The correct answer is 90,000.

Step-by-step explanation:

The number of possible ID numbers can be calculated using the concept of permutations with repetition. Since we have 6 digits in each ID number and each digit can range from 0 to 9, we have 10 choices for each digit. However, 0 cannot be placed as the first digit. Therefore, the first digit can be chosen from 1 to 9, and the remaining 5 digits can be chosen from 0 to 9.

To calculate the total number of ID numbers, we multiply the number of choices for each digit: 9 choices for the first digit and 10 choices for each of the remaining 5 digits, which gives us 9 * 10 * 10 * 10 * 10 * 10 = 90,000.

Therefore, the correct answer is 90,000.