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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
Each of the n digits can be anyone of the three 2,5 or 7.
`therefore`The number of n-digit numbers is `3^(n)`.
`implies3^(n)gt900`
`impliesn=7,8,9` . . .
Hence, smallest value of n is 7.
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