Question

The number of 6-digit numbers that can be made with the digits 1,2,3 and 4 and having exactly two pairs of alike digits is

• A. 480
• B. 540
• C. 1080
• D. none of these

Answer 1

The correct option is C 1080

The number of ways $2$ digits can be selected which will be in pairs =$\left(\begin{array}{c}4\\ 2\end{array}\right)$
Thus, we have $4$ digits ($2$ pairs of alike digits) and $2$ more different digits
Therefore, no. of different 6 digit number =$\left(\begin{array}{c}4\\ 2\end{array}\right)\times \frac{6!}{2!\times 2!}=1080$
Hence, option 'C' is correct.