How many 6-digit numbers can be formed using | vedclass

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Question

(C) The number consists of $2$ pairs of identical digits and $2$ distinct digits.Step $1$: Select the $2$ digits that will form the pairs from the $4$

Vedclass · Accepted Answer

$1080$

Vedclass · Answer

(C) The number consists of $2$ pairs of identical digits and $2$ distinct digits.Step $1$: Select the $2$ digits that will form the pairs from the $4$ available digits: $^4C_2 = 6$ ways.Step $2$: Select the $2$ remaining distinct digits from the remaining $2$ digits: $^2C_2 = 1$ way.Step $3$: Arrange these $6$ digits (where $2$ pairs are identical) in a row: $\frac{6!}{2! 	imes 2!} = \frac{720}{4} = 180$ ways.Total numbers = $6 	imes 1 	imes 180 = 1080$.

How many $6$-digit numbers can be formed using the digits $1, 2, 3,$ and $4$ such that the number contains exactly two pairs of identical digits?

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