Question

# Seven digits from the numbers 1,2,3,4,5,6,7,8 and 9 are written in random order. The probability that this seven digit number is divisible by 9 is:

A
79
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B
19
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C
29!
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D
49
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Solution

## The correct option is B 19Total 7 digit numbers can be formed from the 9 digits = 9P7 There are four exclusive cases of selecting 7 digits out of 9 digits which can from 7 digit numbers which are divisible by 9. 2,3,4,5,6,7,9} 36 removing 1 and 8 1,3,4,5,6,8,9} 36 removing 2 and 7 1,2,4,5,7,8,9} 36 removing 3 and 6 1,2,3,6,7,8,9} 36 removing 4 and 5 All the 7 numbers of each of the 4 sets can be arranged in 7! ways. Hence the favourable number of numbers = 4×7! ∴ Required probability = 4×7!9P7=19.

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