We want to find the number of different entry codes we can make. We need to first choose one single-digit number. Let's list the options we have.
0 1 2 3 4 5 6 7 8 9
There are 10 numbers to pick from, so there are 10 possible options for the first part of the entry code. Next, we need to choose two letters. The English alphabet consists of 26 letters.
A, B, C, D, E, F, G, H, I, J, K, L, M,
N, O, P, Q, R, S, T, U, V, W, X, Y, Z
We have 26 options for choosing the first letter, since the two letter can repeat, we also have 26 options for the second letter. In order to find the total number of all possible codes, we need to use the Fundamental Counting Principle.
Fundamental Counting Principle
If an event M occurs in m ways and event N occurs in n ways, then event M followed by event N can occur in m * n ways.
The Fundamental Counting Principle works also for more than two events. We need to multiply possible choices for all three figures of the code.
Let's substitute the numbers of choices and evaluate the number of possible different entry codes.
10 * 26 * 26 = 6760
