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# The no. of 7 digit numbers that can be formed using the digits $1,2,3,2,3,3,4$ is?

$\begin{array}{1 1} 420 \\ 840 \\ 2520 \\ 5040 \end{array}$

Toolbox:
• No. of arrangement of $n$ things in which $p$ things are of one type and $q$ things are of another type =$\large\frac{n!}{p!.q!}$
There are two $2^s$ and three $3^s$
The required no. of ways = $\large\frac{7!}{2!.3!}=$$420$

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