Math Problem Statement
Solution
The question asks:
"How many different seven-digit telephone numbers can be formed if the first digit cannot be zero?"
Solution:
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First digit: The first digit cannot be zero, so it can be any of the digits from 1 to 9. This gives us 9 possible choices.
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Remaining six digits: Each of these digits can be any number from 0 to 9, giving us 10 choices per digit.
Therefore, the total number of combinations for these six digits is .
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Total combinations: To find the total number of seven-digit telephone numbers, multiply the choices for the first digit by the combinations of the remaining six digits:
Answer:
There are 9,000,000 different seven-digit telephone numbers that can be formed if the first digit cannot be zero.
Would you like to see more details or have any questions?
Here are some related questions:
- How would the total change if the first two digits cannot be zero?
- What if the last digit must also be odd?
- How many combinations would there be if all digits could be repeated except for the first?
- How would the count change if the telephone number must be a palindrome?
- What if a digit cannot appear more than twice in the number?
Tip: When dealing with counting problems, always start by breaking down restrictions step-by-step to ensure accuracy.
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Counting Principles
Formulas
Number of combinations = First digit choices * (Remaining digit choices)^6
Theorems
Fundamental Principle of Counting
Suitable Grade Level
Grades 9-12
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