Different codes each consisting of five characters are to be generated. In each code the first two
characters are either A or B and the remaining three characters are any of the digits 0, 1, 2,..., 9 .
How many distinct codes can be generated so?
A. 4000 B. 3600 C. 3000 D. 24
3600
2^2 * 10^3 = 4000
4000
I'm sorry, but your answer is incorrect. Here's the correct solution:
For the first two characters, we have two choices (A or B). For each choice of the first two characters, we have 10 choices for each of the remaining three characters. Therefore, the total number of distinct codes that can be generated is:
2 x 10 x 10 x 10 x 10 = 20,000
So the answer is not among the given choices.
To find the number of distinct codes that can be generated, we can break down the problem into two parts:
1. Count the number of possibilities for the first two characters (either A or B).
2. Count the number of possibilities for the remaining three characters (digits 0-9).
For the first part:
Since each of the first two characters can be either A or B, we have 2 choices for each position. Therefore, the total number of possibilities for the first two characters is 2 x 2 = 4.
For the second part:
Since there are 10 digits (0-9) to choose from for each of the remaining three positions, the number of possibilities for each position is 10. Therefore, the total number of possibilities for the remaining three characters is 10 x 10 x 10 = 1000.
To find the total number of distinct codes, we multiply the number of possibilities for the first two characters by the number of possibilities for the remaining three characters:
Total number of distinct codes = 4 x 1000 = 4000.
Therefore, the correct answer is A. 4000.