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Standard XII
Mathematics
Classical Definition of Probability
The digits of...
Question
The digits of a nine-digit number are
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
, written in random order, the probability that the number is divisible by
11
is
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Solution
Let the 9 digit number be ABCDEFGHI
Since it is divisible by 11
s=(A+C+E+G+I)-(B+D+F+H) is divisible of 11
Sum of 1,2,3..9 is 45
S=45-2
(B+D+F+H)
9<
(B+D+F+H)<31
S is a odd number between -15,25
So only multiple of 11 in -15 to 25 are 11,-11
Total selection =
9
C
4
=126
In this only 11 satisfies the solution
So probability=11/126
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