Question

Locker codes at Lincoln High School consist of 4 digits. No digit can be used more than once. How many locker codes are available at Lincoln High School? A 210 B 3,024 C 5,040 D 10,000

Answer 1

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:

`10*9*8*7\text{ = 5040}`

Therefore, there are a total of 5040 available locker codes at Lincoln High School

Correct answer = Option C