Question

The chairs of an auditorium are to be labeled with an uppercase English letter followed by a positive integer not exceeding 200. For example, A 000, B 123, Z 200 are three possible seat labels. What is the largest number of chairs that can be labeled differently?

A) 26,200
B) 200,000
C) 52,000
D) 40,000

Answer 1

The largest number of chairs that can be labeled differently is 52,000.

Step-by-step explanation:

The chairs in the auditorium can be labeled using an uppercase English letter followed by a positive integer not exceeding 200. Therefore, there are 26 possible uppercase English letters that can be used as labels. For the positive integer part, it can range from 1 to 200, giving us a maximum of 200 different options.

To find the largest number of chairs that can be labeled differently, we need to multiply the number of possible uppercase English letters (26) by the maximum possible positive integer (200). This gives us a total of 26 * 200 = 5200 different chairs that can be labeled differently.

Therefore, the correct answer is C) 52,000.