Question 1183743
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The other tutor goes through a lengthy explanation of why there are only 24 possible sequences (permutations) of the last three digits, so that the probability of getting the right password on the first attempt is 1/24.<br>
That is quite possibly the answer the author of the problem wanted; however, grammatically it is not the right answer.<br>
The problem is with the phrasing of the question, which says the three last digits are "even and not the same".<br>
That does NOT mean the same thing as "even and all different".  For example, the digits 224 are all even and not the same....<br>
So with the way the problem is stated, the only sequences NOT allowed are 222, 444, 666, and 888.<br>
Without restrictions, the number of possible permutations of the last three digits is 4*4*4=64; with the 4 excluded ones, the number of allowable permutations is 64-4=60.  And of course only one of them is the correct one.<br>
ANSWER: The probability of entering the correct password on the first try is 1/60.<br>