There are 3,265,920 possible 9-digit numbers that can be formed using different digits.
Here's how we arrive at that answer:
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Understanding the Constraints: We need to form a 9-digit number using distinct digits (0-9), meaning no digit can be repeated. The first digit cannot be zero.
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Breaking Down the Problem: We consider each digit place value individually.
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First Digit: The first digit can be any number from 1 to 9. So there are 9 choices.
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Second Digit: Now we have used one digit. We can use 0, but not the digit chosen for the first place. This gives us 9 choices again.
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Third Digit: We've used two digits. So we have 8 remaining choices.
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Fourth Digit: We've used three digits. So we have 7 remaining choices.
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Fifth Digit: We've used four digits. So we have 6 remaining choices.
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Sixth Digit: We've used five digits. So we have 5 remaining choices.
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Seventh Digit: We've used six digits. So we have 4 remaining choices.
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Eighth Digit: We've used seven digits. So we have 3 remaining choices.
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Ninth Digit: We've used eight digits. So we have 2 remaining choices.
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Calculation: To find the total number of possible 9-digit numbers, we multiply the number of choices for each digit place:
9 9 8 7 6 5 4 3 2 = 3,265,920
Therefore, 3,265,920 different 9-digit numbers can be formed using different digits.
