Given Digits 2, 2, 3, 3, 3, 4, 4, 4, 4. How many distinct 4 digit
Given Digits 2, 2, 3, 3, 3, 4, 4, 4, 4. How many distinct 4 digit numbers greater than 3000 can be formed using these digits?
A. 50
B. 51
C. 52
D. 54
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
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