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

6
7
8
9

Answer 1

for such condition 3^n >900
3^6=729
and 3^7=2187
thus least value of n=7

Answer 2

Answer:

Option 2 - 7

Step-by-step explanation:

Given : 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.

To find : The smallest value of n for which this is possible is ?

Solution :

An n-digit number is a positive number with exactly n digits.

For one's spot we have 3 digit,

For second's spot we have 3 digit,

For nth spot we have 3 digit,

The total number of ways to make an n-digit number with only 2,5 and 7 is going to be $3^n$

According to question,

$3^n\geq 900$

$\frac{3^n}{3^2}\geq 100$

$3^{n-2}\geq 100$

The value of n in which it is greater than 100.

$3^4=81$ and $3^5=243$

Which means $n-2\geq 5$

$n\geq 7$

The smallest value of n for which this is possible is 7.

Therefore, Option 2 is correct.