How Many 5-Digit Telephone Numbers Can Be Constructed?

When we talk about 5-digit telephone numbers, we are considering a sequence of five digits where each digit can be any number from 0 to 9. In most cases, telephone numbers are treated as strings of digits rather than numerical values. This means that numbers with leading zeros (like 01234) are perfectly acceptable.

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Step-by-Step Explanation

1. Each Digit’s Possibilities

• Digits Available:
  Each of the five positions in the telephone number can be filled with any one of the 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

2. Applying the Multiplication Principle

• Independence of Positions:
  Since each digit is chosen independently, the total number of combinations is the product of the number of choices for each position.
• Calculation:
  For each of the 5 positions, there are 10 possible choices. Therefore, the total number of 5-digit telephone numbers is: 10×10×10×10×10=105=100 000.10 \times 10 \times 10 \times 10 \times 10 = 10^5 = 100\,000.

3. No Restrictions on Leading Zeros

• Telephone Number Context:
  In telephone numbers, leading zeros are allowed. This is why a sequence like 01234 is counted as a valid 5-digit telephone number.

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Conclusion

Since each of the 5 positions in a telephone number can be filled with any of 10 digits (0–9), and there are no restrictions like excluding leading zeros, the total number of 5-digit telephone numbers that can be constructed is: 105=100,000.\textbf{10}^5 = \textbf{100,000}.

This means there are 100,000 possible 5-digit telephone numbers.

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