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If ABCD be any random 4-digit number in base 11, what is the probability that A < B < C < D?

How i can achieve this? Thanks in advance.

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    Depends. We allowing leading zeros?2012-05-07
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    No..It must be a 4 digit.No leading zeros.2012-05-07
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    This changes the problem then.2012-05-07

1 Answers 1

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The desired probability is just the number of four-digit numbers of the desired type divided by the total number of four-digit numbers.

In base eleven there are eleven possible digits. The first digit of a four-digit number can be any of the ten digits other than $0$, and each of the other three can be any of the $11$ digits, so there are $10\cdot11^3$ possible four-digit numbers.

If $ABCD$ is a four-digit number in which $A

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    This is restating the question.2012-05-07
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    @Neil: No, it's providing a very large hint by doing most of the problem and leaving the last step or to for vikiiii to finish.2012-05-07
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    @Neil: No. $ $ $ $2012-05-07