A company uses one letter followed by four digits for product codes. If any of the
letters A–Z is allowed in the first position, and any of the digits 0–9 in the next four
positions, how many different product codes are possible? (The letters and digits may be used more than once.)
AAAaannndd the bot gets it wrong yet again!
26 x 10 x 10 x 10 x 10 = 260,000
My apologies for the mistake. You are correct that the total number of different possible product codes is:
26 x 10 x 10 x 10 x 10 = 260,000
Thank you for pointing out my error.
To calculate the number of different product codes possible, we need to determine the number of options for each position and then multiply them together.
In this case, the first position can have any of the 26 letters from A to Z. So, there are 26 options for the first position.
The next four positions can have any of the 10 digits from 0 to 9. So, there are 10 options for each of the next four positions.
To calculate the total number of different product codes, we multiply the number of options for each position together:
Total = Options for the first position × Options for the second position × Options for the third position × Options for the fourth position × Options for the fifth position.
Total = 26 × 10 × 10 × 10 × 10 = 260,000.
Therefore, there are 260,000 different product codes possible in this case.
There are 26 choices for the first letter and 10 choices for each of the four remaining digits. Thus, the total number of different product codes is:
26 x 10 x 10 x 10 x 10 = 26,000
Therefore, there are 26,000 different possible product codes.