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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
An eight digit number divisible by $9$ is to be formed by using $8$ digits out of the digits $0,1,\ldots,9$ without replacement.
The number of ways in which this can be done is
Solution
Sum of digits must be divisible by $9$. Total sum of digits $0$ to $9$ is $45$. Choose $8$ digits such that their sum is divisible by $9$. Possible digit-exclusions give $4$ valid cases. Arrangements of remaining $8$ digits excluding leading zero restriction gives $4\times7!$ Answer: $\boxed{4(7!)}$Online Test Series, Information About Examination,
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