Question

a computer applications teacher asks the class to write a program to create a list of computer codes for labeling the computers at the school. each code must begin with an uppercase (capital) letter from the 26 - letter english alphabet, followed by 5 digits. the digits may be repeated, but the code cannot end in 0 or 1. how many codes can be created?
competency c13
options: 338915776, 2360000, 696000, 786240

Explanation:

Step1: Determine the number of choices for the first character (uppercase letter)

There are 26 uppercase letters in the English alphabet, so there are 26 choices for the first character.

Step2: Determine the number of choices for the first four digits

Each of the first four digits can be any digit from 0 - 9, so there are 10 choices for each of these four positions. So the number of choices for the first four digits is $10\times10\times10\times10 = 10^{4}$.

Step3: Determine the number of choices for the fifth digit

The fifth digit cannot be 0 or 1, so there are $10 - 2=8$ choices for the fifth digit.

Step4: Calculate the total number of codes

Using the multiplication principle, we multiply the number of choices for each part together. So the total number of codes is $26\times10^{4}\times8$.
First, calculate $10^{4}=10000$. Then $26\times10000 = 260000$. Then $260000\times8=2080000$.

Answer:

2,080,000 (corresponding to the option with this value, assuming the option is labeled appropriately, e.g., if one of the options is "2,080,000", that is the correct one)