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How Many 7-Digit Numbers Contain Exactly One Digit 7?

Discover how to calculate the number of 7-digit numbers containing exactly one 7 using combinatorial methods and digit placement rules.

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Video transcript

Assuming the number is a 7-digit number composed of natural numbers: There are 1,000,000 possible combinations. If you need to place exactly one 7 in the 7-digit number, there are 6 other places for the remaining digits (1-6). Therefore, the total is  × 9^6 = 531,441 (since 1-6 can be any digit from 0-9 except 7, offering 9 choices for each location).

Questions and answers

  1. How do you calculate numbers with exactly one specific digit?

    To calculate numbers with exactly one specific digit, first choose the position for that digit, then fill the remaining positions with allowed digits excluding that digit, using combinatorial multiplication.

  2. What is the total number of 7-digit numbers?

    The total number of 7-digit numbers ranges from 1,000,000 to 9,999,999, giving 9,000,000 possible numbers.

  3. Why are digits other than 7 limited in this calculation?

    Other digits are limited to exclude 7 to ensure only exactly one digit 7 appears in the number, maintaining the condition of the problem.

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