First slide

Permutations

Question

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

Moderate

A

6
B

7
C

8
D

9

Solution

Distinct n digit numbers which can be formed using digits 2, 5 and 7 are 3n . We have to find n so that
$\begin{array}{l} 3^{n} \geq 900 \Rightarrow 3^{n - 2} \geq 100 \\ \Rightarrow n - 2 \geq 5 or n \geq 7 \end{array}$
So, the least value of n is 7.

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