21. The apartments in Greg's building are named using the letters A, B, C, and D and the digits 1 through 9. How many apartments are there in Greg's building if each apartment is named by a single letter followed by a single digit?
Answer: A
There are 36 apartments in Greg's building.
Each apartment name consists of one letter and one digit, where the letters are A, B, C, and D (4 options) and the digits are 1 through 9 (9 options). Therefore, the total number of apartments is calculated by multiplying the number of letter options by the number of digit options: 4 letters × 9 digits = 36 apartments.
A) 36
This option is correct because it accurately represents the total number of unique combinations of letters and digits. With 4 letters and 9 digits, the calculation shows that 4 × 9 equals 36.
B) 16
This option is incorrect as it does not reflect the correct number of combinations. The product of the options (4 and 9) yields a significantly higher total than 16, indicating a misunderstanding of the calculation involved.
C) 40
This option is incorrect because it exceeds the total number of combinations possible with the given letters and digits. The calculation shows that 4 letters multiplied by 9 digits only results in 36, not 40.
D) 13
This option is also incorrect as it underestimates the total number of apartments. The combination of 4 letters and 9 digits cannot yield a total of only 13 apartments, as the calculation clearly shows a larger number.
Conclusion
The correct answer is 36, as it is derived from the valid combinations of the letters and digits available for naming the apartments. All other options are incorrect due to miscalculations or misunderstandings of the combination process. Thus, option A is definitively the only correct choice.