Question

The access code for a car's security system consists of 5 digits. Each digit can be any number from 0 through 9. Use the Fundamental Counting Principle (FCP) to find the number of outcomes if each digit is used only once and not repeated.​

Answer 1

The number of outcomes for the car's security system access code using the Fundamental Counting Principle is 30,240.

Step-by-step explanation:

The number of outcomes can be found using the Fundamental Counting Principle (FCP). FCP states that if there are n ways to do one thing and m ways to do another thing, then there are n x m ways to do both things together.

In this case, each digit in the access code can be selected from 0 to 9, resulting in 10 choices for the first digit. After selecting the first digit, there are 9 choices left for the second digit (since it cannot be the same as the first digit), and so on.

Therefore, the number of outcomes can be calculated as: 10 x 9 x 8 x 7 x 6 = 30,240