Question

A shopkeeper sells house numbers. She has a large supply of the numerals 4, 7, and 8, but no other numerals. How many different three-digit house numbers could be made using only the numerals in her supply?

Answer 1

There are 27 different three-digit house numbers that can be made using only the numerals 4, 7, and 8, as there are 3 choices for each digit and there are 3 digits in total.

Step-by-step explanation:

The question asks how many different three-digit house numbers could be made using only the numerals 4, 7, and 8 from a shopkeeper's supply. To determine this, we need to calculate the possible combinations for a three-digit number where each digit can be one of three possibilities. For each position (hundreds, tens, and ones), there are three choices (4, 7, or 8), which means we multiply the number of choices for each digit. So, we calculate 3 (choices for the first digit) × 3 (choices for the second digit) × 3 (choices for the third digit).

The calculation would be:

1. First digit: 3 possible numbers (4, 7, or 8)
2. Second digit: 3 possible numbers (4, 7, or 8)
3. Third digit: 3 possible numbers (4, 7, or 8)

Therefore, the number of different three-digit house numbers she can make is 3 × 3 × 3 = 27 different house numbers.