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An n-digit number is a positive numbe...

An n-digit number is a positive number with exactly `n` digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5, and 7. The smallest value of `n` for which this is possible is a.`6` b. `7` c. `8` d. `9`

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The correct Answer is:
7
Distinct n-digit numbers which can be formed using digits 2,5 and 7 are `3^(n)` since each place can be filled in 3 ways.
We have to find n so that `3^(n) ge 900`
`implies 3^(n-2) ge 100`
`implies n-2 ge 5`
`implies n ge 7`.
So, the least value of n is 7.
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