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 digits, is

• A. $480$
• B. $540$
• C. $1080$
• D. $2040$

Answer 1

Answer: (C)

$1080$

The number of 6 digits has two pairs of digits and 2 different digits.
The number of ways of selecting 2 digits for two pairs and 2 other digits
$={{}^{4}C}_2\times {{}^{2}C}_2$
Now, we arrange these six digits which consists of two pairs and 2 different digits. This can be done in $\frac{6!}{2!2!}$ ways
$\therefore$ Required number of numbers
$={{}^{4}C}_2\times {{}^{2}C}_2\times \frac{6!}{2!2!}=1080$