Question

Each badge will begin with the letter P, Q, R, or S followed by 2 digits. The company presently has 250 employees who will need badges. How many different badges are possible? Will this ID code system provide enough different codes for the employees?

Answer 1

The number of different badges possible is 400, calculated by multiplying the number of letter options (4) by the number of digit options for each of the two digits (10 each), thus, there are enough unique IDs for all 250 employees.

Step-by-step explanation:

The student's question revolves around the number of unique badge identifications (IDs) that can be created using a specific format. Each badge ID will begin with a letter (P, Q, R, or S) followed by two digits. To calculate the total number of different badges possible, we need to consider all the possible combinations that can be made using these constraints.

There are 4 choices for the first letter (P, Q, R, or S). Since each badge is then followed by two digits and there are 10 possible digits (0-9) for each position, there are 10 choices for the second character and 10 choices for the third character. To find the total number of combinations we multiply the number of choices for each position:

4 (letters) x 10 (first digit) x 10 (second digit) = 400 total combinations.

Comparing this to the number of employees, the company has 250 employees and needs 250 unique badge IDs. Since the number of different badges possible (400) exceeds the number of employees, this ID code system provides enough different codes for all the employees.