Answer to Question #233647 in Statistics and Probability for Uyu

Question

Student numbers at a certain university consist of 7 digits followed by a single letter. The first 2 digits are the year of first registration. The next digit is either a 0 or a 1. The next 4 digits are randomly selected numbers, followed by a randomly selected letter. How many student numbers are possible between 2017 and 2020 (both inclusive)?

Answer 1

The first two places can be either 17 or 18 or 19 or 20.

So, the first two places can be filled in 4 ways.

The third place can be filled with 2 ways (0 or 1).

In the next four places, each place can be filled with 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

The last place can be filled in 26 ways (26 letters).

Total students number possible = (ways to fill the first two places) $\times$ (ways to fill the thirs place) $\times$ (ways to fill the fourth) $\times$ (ways to fill the 5^th) $\times$ (ways to fill the 6^th) $\times$ (ways to fill the 7^th) $\times$ (ways to fill the last place)

$= 4 \times 2 \times 10 \times 10 \times 10 \times 10 \times 26 \\ = 2080000$

There are 2080000 possible student numbers.