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Question Number 135861 by liberty last updated on 16/Mar/21
Probability  Digits from 1 to 9 are randomly placed to form a 9-digit number. What is the probability that the number is divisible by 18?
ProbabilityDigits from 1 to 9 are randomly placed to form a 9-digit number. What is the probability that the number is divisible by 18?
Answered by EDWIN88 last updated on 16/Mar/21
To be divisible by 18, the number must be  divisible by 2 and 9. The sum of digits is  1+2+3+4+...+9 = ((9×10)/2) = 45 which is   divisible by 9, There are 9 digits of which are  even (2,4,6,8) . So the probability that the  number is divisible by 18 is (4/9)
Tobedivisibleby18,thenumbermustbedivisibleby2and9.Thesumofdigitsis1+2+3+4++9=9×102=45whichisdivisibleby9,Thereare9digitsofwhichareeven(2,4,6,8).Sotheprobabilitythatthenumberisdivisibleby18is49

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