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Step-by-Step Solution
Step 1: Identify the Digits Available
We have the digits 0, 2, 4, 6, and 8 to form the required numbers.
Step 2: Determine the Conditions for the Number
The question asks for numbers greater than 10,000. This implies we must form 5-digit numbers (since any 4-digit or smaller number would be less than 10,000). Also, the first digit (most significant digit) cannot be 0, because that would result in a 4-digit number.
Step 3: Count the Possible 5-Digit Numbers
• The first digit can be chosen in 4 ways (2, 4, 6, or 8).
• After choosing the first digit, we have 4 remaining digits (including 0 if it was not used) for the second position.
• Then 3 remaining choices for the third digit.
• Then 2 remaining choices for the fourth digit.
• Finally, 1 choice for the fifth digit.
Thus, the total number of such 5-digit numbers is
4 \times 4 \times 3 \times 2 \times 1 = 96 .
Step 4: Final Answer
The number of all numbers greater than 10,000 formed under these conditions is 96.
Reference Image for the Solution
