What is the value of the determinant | array lll 1! & 2! & 3! 2! &...

\left|$$\begin{array}{lll}1! & 2! & 3! \\ 2! & 3! & 4! \\ 3! & 4! & 5!\end{array}$$\right| Taking 2! common from $C_2$ and 3 ! common from C_3\Rightarrow 2!\cdot 3!\left|$\begin{array}{ccc} 1 & 1 & 1 \\ 2 & 3 & 4 \\ 6 & 12 & 20 \end{array}$\right|$ On expanding, we get\begin{aligned} & 12 \times[1(60-48)-1(40-24)+1(24-18)] \\ & =12 \times[12-16+6] \\ & =12 \times 2=24 \end{aligned}$$$