Subjects combinatorics

Auditorium Labels 4Af78D

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1. **State the problem:** We need to find how many distinct labels are possible for auditorium chairs, where each label consists of one uppercase letter followed by an integer from 1 to 100. 2. **Identify the components:** - There are 26 uppercase letters (A to Z). - The integer part can be any number from 1 to 100, so there are 100 possible numbers. 3. **Formula used:** The total number of distinct labels is the product of the number of letter options and the number of number options. $$\text{Total labels} = 26 \times 100$$ 4. **Calculate:** $$26 \times 100 = 2600$$ 5. **Conclusion:** There are 2600 distinct labels possible.