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An n digit number is a positive number ...

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 is possible is

A

6

B

7

C

8

D

9

Text Solution

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The correct Answer is:
B
Each place can be filled in 3 ways
`:.` n places can be filled in `3^n :. 3^n ge 900`
`:. 3^6 = 729 and 3^7 = 2187` Hence n =7.
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