Question

1. Student ID number at a certain University are made up of a letter, followed by six 1-digit

numbers, and then another letter (example: L132389M). How many student ID numbers are
possible if the letters cannot be repeated? [4 points]

Answer 1

650,000,000 student ID numbers are possible if the letters cannot be repeated.

Explanation:

The order in which the digits or letters are placed is important, which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

In this question:

2 letters from a set of 26(permutations, as letters cannot be repeated).

6 digits, each with 10 possible outcomes.

How many student ID numbers are possible if the letters cannot be repeated?

`T = 10^6 * (26!)/(24!) = 650000000`

650,000,000 student ID numbers are possible if the letters cannot be repeated.