A) \[\frac{2}{9}\]
B) \[\frac{1}{5}\]
C) \[\frac{1}{3}\]
D) \[\frac{1}{9}\]
Correct Answer: D
Solution :
The number is divisible by 9, if the sum of the digits is divisible by 9. The seven digits number which is divisible by 9 are \[\{2,3,4,5,6,7,9\},\,\,\{1,3,4,5,6,8,9\}\] \[\{1,2,4,5,7,8,9\}\] and \[\{1,2,3,6,7,8,9\}\] \[\therefore \] Required probability \[=\frac{4\times 7!}{^{9}{{C}_{7}}\times 7!}=\frac{4}{\frac{9\times 8}{2\times 1}}\] \[=\frac{1}{9}\]
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