Question

an oil company is going to issue new id codes to its employees. each code will have one letter, followed by one digit, followed by three letters. the letters w, x, y, and z will not be used. so, there are 22 letters and 10 digits that will be used. assume that the letters can be repeated. how many employee id codes can be generated?

Explanation:

Step1: Count options for first character

There are 22 valid letters, so number of choices = $22$

Step2: Count options for the digit

There are 10 valid digits, so number of choices = $10$

Step3: Count options for each of 3 letters

Each of the 3 final positions has 22 letter choices, so total for these = $22 \times 22 \times 22 = 22^3$

Step4: Calculate total number of codes

Multiply all independent choices together: $22 \times 10 \times 22^3 = 10 \times 22^4$
Calculate $22^4 = 22\times22\times22\times22 = 484\times484 = 234256$
Then $10 \times 234256 = 2342560$

Answer:

2342560