# Seven digits from the digits 1,2,3,4,5,6,7,8,9 are written in random order. the probability that this seven digit no. is divisible by 9 is ?

1
by namku

2015-05-13T18:39:01+05:30

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Recall the fact that an integer is divisible by if the sum of its digits is divisible by .

Since the sum of first natural numbers is , which is divisible by , it must be the case that the sum of the two integers that we don't pick to form the seven digit number is divisible by .

Number of ways of choosing two integers from integers :

Number of two digit pairs whose sum is divisible by :

Simply take the ratio to get the probability that the seven digit number so formed is divisible by
:) basically we're using this :
"9m - n" is divisible by 9 only if "n" is divisible by 9
because, 9m - n = 9t implies n = 9m-9t = 9(m-t)
which simply means that "n" is a multiple of 9
right. tha'ts interesting ! thanks a lot, AGAIN !