What are the odds of guessing a (randomly generated) sequence of four numbers out of the sequence 0-9?

The question says it as clearly as I can think of trying to explain it. Same principle as the lottery odds (eg 1 in X million) but with four numbers out of a possible 10 (0-9). I suppose it is based on the possible permutations of four number sequences.What are the odds of guessing a (randomly generated) sequence of four numbers out of the sequence 0-9?
Im amazing so 100%What are the odds of guessing a (randomly generated) sequence of four numbers out of the sequence 0-9?
Hi! EVERYONE IS WRONG! People are assuming ODDS and PROBABILITY are the same thing. Anyway, I have your answer. I just also want to say that getting an answer is very easy, but your question is also very fuzzy!





For instance, what if we chose 4444? Is this a possible sequence, or do you NOT WANT numbers to be repeated?





Oftentimes, these sorts of questions involve sequences where a number cannot be repeated.





Anyway, just to make sure you have the right answer, I will answer your question in TWO WAYS. First way will involve numbers that CANNOT be repeated. Second way will involve numbers that CAN be repeated.





FIRST WAY:





If numbers cannot be repeated, then there are 10x9x8x7 different ways of having a 4 number sequence. Since there is only 1 way of getting this sequence correct, the ODDS are:





1 / 5039.





BE CAREFUL, this is the correct answer because Odds are NOT the same as probability. If you asked for probability, then it would be 1/5040.











SECOND WAY





If numbers CAN be repeated, then there are 10000 different ways of having a 4 number sequence. Since there is only 1 way of getting the sequence correct, the ODDS are:





1/9999. Again, ODDS and probability are NOT the same. If you asked for probability, then it would be 1/10000.





I hope this helps!
if position of the individual numbers in the sequence doesn't matter, then the odds of guessing 1 sequence containing four numbers is 1/10C4( read as 10 combination four), if otherwise, the odds is 1/10P4(10 permutation four). the odds of the latter case is lower than the first.
Each number reduces the possible pool of numbers by one, such that the chances for one number is 10, two is 10 x 9, and so forth. So the answer would be 10 x 9 x 8 x 7 which is 1 in 5040, it can also be written as 1 in 10!/(10-4)!
It is actually not the same principle as the lottery because you can use each digit more than once (whereas in the lottery all the numbers are different).





First digit: 10 possibilities


Second digit: 10 possibilities


And so for the third and fourth digits.





10*10*10*10=10,000





Odds are 1:10,000.
well, the biggest number is 9999, so you have a 1 in 10000 (got to count zero as being a case too) chance of guessing that number.
10! / (6! 4!) = 210

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