How many numbers can be made with digits 0, 5, 9 which are greater than 0 and less than a million?
Question
How many numbers can be made with digits 0, 5, 9 which are greater than 0 and less than a million?
Solution
To solve this problem, we need to consider the different cases for the number of digits in the number we are forming.
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One-digit numbers: There are 2 possible numbers (5 and 9). Zero is not considered because the number must be greater than zero.
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Two-digit numbers: The first digit can be either 5 or 9 (2 possibilities), and the second digit can be 0, 5, or 9 (3 possibilities). So there are 2*3 = 6 possible two-digit numbers.
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Three-digit numbers: The first digit can be either 5 or 9 (2 possibilities), and the second and third digits can be 0, 5, or 9 (3 possibilities each). So there are 233 = 18 possible three-digit numbers.
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Four-digit numbers: The first digit can be either 5 or 9 (2 possibilities), and the second, third, and fourth digits can be 0, 5, or 9 (3 possibilities each). So there are 233*3 = 54 possible four-digit numbers.
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Five-digit numbers: The first digit can be either 5 or 9 (2 possibilities), and the second, third, fourth, and fifth digits can be 0, 5, or 9 (3 possibilities each). So there are 23333 = 162 possible five-digit numbers.
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Six-digit numbers: The first digit can be either 5 or 9 (2 possibilities), and the second, third, fourth, fifth, and sixth digits can be 0, 5, or 9 (3 possibilities each). So there are 23333*3 = 486 possible six-digit numbers.
Adding up all these possibilities, we find that there are 2 + 6 + 18 + 54 + 162 + 486 = 728 numbers that can be made with the digits 0, 5, and 9 that are greater than 0 and less than a million.
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