Question

14. A brand-new school district needs to generate ID numbers for its student body. The district anticipates a total

enrollment of 75,000 students within the next ten years. Will a five-digit ID number using the symbols 0, 1,…, 9
be enough? Explain your reasoning.

Answer 1

Yes, it will be enough.

Explanation:

In this problem, we must check if the number of all possible variations of the five-digit ID code will be greater than the expected 75,000 students.

If all the numeric symbols from 0 to 9 will be used in the ID, there are ten possible values for each of the five digits. Therefore, the total number of possibilities (N) can be determined as follows:

`N=10*10*10*10*10\\N=100,000\\`

Since the total number of possible five-digit IDs is bigger than the expected number of students, this system will be enough.