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:

Options

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

Explanation

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)xx""^(2)C_(2)`. Now, we arrange these six digits which consists of two pairs and 2 different digits. This can be done in `(6!)/(2!2!)` ways.
`:.` Required numbers `=""^(4)C_(2)xx""^(2)C_(2)xx(6!)/(2!2!)=1080`.