Question:
If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _____________.
If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10,000 is equal to _____________.
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With only five distinct digits and no repetition, a number above 10,000 must be a 5-digit number using all the digits, with a non-zero first digit.
Updated On: Nov 4, 2026
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Correct Answer: 96
Solution and Explanation
With no repetition, a number can have at most 5 digits. A number greater than 10,000 must therefore be a 5-digit number, which uses all of 0, 2, 4, 6, 8 exactly once. The first digit cannot be 0.
First digit: 4 choices (2, 4, 6, 8). The remaining 4 positions use the other 4 digits in \(4! = 24\) ways.
Count \(= 4 \times 24 = 96\). (Every such number is at least 20468, so it exceeds 10,000.)
Answer: 96
First digit: 4 choices (2, 4, 6, 8). The remaining 4 positions use the other 4 digits in \(4! = 24\) ways.
Count \(= 4 \times 24 = 96\). (Every such number is at least 20468, so it exceeds 10,000.)
Answer: 96
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