The digits from 1 to 6 are arranged to form a six-digit multiple of 5. What is the probability that the number is greater than 500,000? Express your answer as a common fraction.

 Aug 14, 2018
edited by ColdplayMX  Aug 14, 2018

Here's the way I see this........


If the number is a multiple of 5, it must end in a  "5"......and there are 5!  =  120  ways of arranging the other digits


Of the numbers of interest.....the "6" has to be the first digit if the number is > 500,000 and the "5" has to be the last


Thus....the "middle digits" in these numbers can be arranged in 4!  = 24 ways


So...the probability is  24 / 120   = 1 / 5


Edited to correct an earlier answer......



cool cool cool

 Aug 14, 2018
edited by CPhill  Aug 15, 2018
edited by CPhill  Aug 15, 2018

Actually the right answer is 1/6 because there is only one digit that works, and that is the 6. Therefore the probability is 1/6. Technically, you could generate all those outcomes for each digit. I believe that the correct answer is 1/6.

 Aug 14, 2018



The generated numbers are constrained to multiples of five, so (5) has to be used in the units position. This leaves five (5) numbers [1,2,3,4,6] to choose for the first digit, and six (6) is the only number that produces numbers greater than 500,000.  (The arrangement of the remaining numbers are irrelevant.)


The probability is 1/5




 Aug 14, 2018
edited by GingerAle  Aug 14, 2018

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