Question

How many different license plates are possible if a plate consists of three digits followed by 3 letters? Both numbers and letters can be used more than once.

A) 103,263
B) 310,326
C) 10,9,8,26,25,24
D) 30,78
E) 4,978

Answer 1

The number of different license plates possible with three digits followed by three letters is obtained by calculating the permutations for each part (1,000 for digits and 17,576 for letters) and then multiplying them together, resulting in 17,576,000 different license plates.

Step-by-step explanation:

The subject of this question is combinatorics, which is a branch of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. To find the number of possible license plates that consist of three digits followed by three letters, we will calculate the permutations for each part and then multiply them together since each digit and letter can be chosen independently of the others.

For the three digits, as each position can contain any digit from 0 to 9, there are 10 options for each of the three positions. Thus, the number of permutations for the digits is 10 x 10 x 10, which is 1,000 combinations.

For the three letters, each position can contain any letter from A to Z, which gives us 26 options for each of the three positions. Thus, the permutations for the letters are 26 x 26 x 26, which is 17,576 combinations. To find the total number of possible license plates, we multiply the digit combinations by the letter combinations: 1,000 x 17,576, which equals 17,576,000 different possible license plates.