4 digit number knowing one number

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The discussion focuses on calculating the total number of possible 4-digit combinations when one digit is known but its position is uncertain. The known digit can occupy one of four slots, leading to four potential placements. For the remaining three slots, each can be filled with any of the 10 digits (0-9), resulting in a calculation of 4 times 10 cubed (10^3). Therefore, the total number of combinations is 4 x 1000, equating to 4000 possible 4-digit numbers.

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I can't get started on this. If I am trying to figure out a 4-digit number, and I know one of the numbers, but not which digit it is, how many possible numbers are there?
Thanks!
 
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Welcome to PF.
The trick is to think of it like this: you have four slots which can take a single digit each - the four digits make one number.

There are four possible places that the known digit can be in.
So the answer must be four times the number of ways that the remaining three digits can be arranged.
There are 10 possible digits.

Presumably you have just been doing permutations and combinations?
 
annenap said:
If I am trying to figure out a 4-digit number,
and I know one of the numbers [digits], but not which digit it is,
how many possible numbers are there?

I have questions.

Is this digit you know different from all of the other digits?



You are not allowing 0 for a first digit?
 

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