Solve the problem.
-If a license plate consists of four digits, how many different licenses could be created having at least one digit repeated.
A)5040 licenses
B)4960 licenses
C)3024 licenses
D)10,000 licenses

Question

Quizplus · Accepted Answer

The total number of possible license plates with four digits (each digit can be from 0 to 9) is $10^4 = 10,000$. To find the number of licenses with at least one digit repeated, subtract the number of licenses with all unique digits from the total. There are 10 options for the first digit, 9 for the second (excluding the first digit), 8 for the third, and 7 for the fourth, giving $10 \times 9 \times 8 \times 7 = 5040$ unique digit licenses. Subtracting this from the total gives $10,000 - 5040 = 4960$ licenses with at least one digit repeated.

Solve the Problem. -If a License Plate Consists of Four Digits, How Many