To obtain the number of locker codes available, the following steps are necessary:
Step 1: Create a diagram to represent the slot for each of the digits, as below;
Step 2: State the number ways that each digit can be used to fill any of the spots, as below:
Given that there are the numbers 0,1,2,3,4,5,6,7,8,9 - a total of 10 numbers,
- The first slot can be filled with any of the digits above, and thus can be filled in 10 ways
- The second slot can be filled with any of the remaining 9 numbers after one of them has already been used to fill the first slot. Thus, there are 9 ways the second slot can be filled.
- The same line of reasoning tells us that the third slot will be filled in 8 ways
- Lastly, the fourth slot will be filled in 7 ways
The diagram below gives a better illustration:
Step 3: Multiply the numbers of ways to find the total number of locker codes that are available, as follows:
[tex]10\times9\times8\times7\text{ = 5040}[/tex]Therefore, there are a total of 5040 available locker codes at Lincoln High School
Correct answer = Option C
