# 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 ?

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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 :

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

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 :