Correct Answer - Option 2 : 51
Given digits: 2, 2, 3, 3, 3, 4, 4, 4, 4
Case 1:
The first digit is 4.
4 _ _ _
Rest of the places are filled by 2, 2, 3, 3, 3, 4, 4, 4
\( \Rightarrow \begin{array}{*{20}{c}} 4&\_&\_&\_\\ \downarrow & \downarrow & \downarrow & \downarrow \\ 1&3&3&3 \end{array}\)
The no. of cases = 1 × 3 × 3 × 3 – 1 = 26
Case 2:
The first digit is 3:
Rest of the places are filled by 2, 2, 3, 3, 4, 4, 4, 4
The exception cases are = 222, 333
Therefore:\(\begin{array}{*{20}{c}} 3&\_&\_&\_\\ \downarrow & \downarrow & \downarrow & \downarrow \\ 1&3&3&3 \end{array}\)
No. of cases = 1 × 3 × 3 × 3 – 2
= 25
Case 3:
First digit is 2
No number can be possible which is greater than 3000
Total no. of cases = 26 + 25 = 51
