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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`

A

6

B

7

C

8

D

9

Text Solution

Verified by Experts

There are three ways to fill up each place. So, n places can be filled in `3^(n)` ways.
Hence, total number of n digit numbers = `3^(n)`.
Now, `3^(n)ge900impliesnge7`
Hence, the smallest value of n is 7.
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