There are 7 Telugu books and 4 Hindi books. From those in how many ways can 4 Telugu and 1Hindi book be arranged so that the Hindi book is always at the middle is

$$\begin{gathered} \mathrm{Total} \mathrm{no}.\mathrm{of} \mathrm{telugu} \mathrm{books} = 7. \\ \mathrm{Total} \mathrm{no}.\mathrm{of} \mathrm{hindi} \mathrm{books} =4. \end{gathered}$$

$$\begin{gathered} \mathrm{No}.\mathrm{of} \mathrm{ways} \mathrm{of} \mathrm{selecting} 4 \mathrm{telugu} \mathrm{books} = {}^7\mathrm{C}_4. \\ \mathrm{No}.\mathrm{of} \mathrm{ways} \mathrm{of} \mathrm{selecting} 1 \mathrm{hindi} \mathrm{book} ={}^4\mathrm{C}_1 \end{gathered}$$

$$\begin{gathered} 5 \mathrm{books} \mathrm{are} \mathrm{to} \mathrm{be} \mathrm{arranged} \mathrm{such} \mathrm{that} \\ \mathrm{hindi} \mathrm{is} \mathrm{always} \mathrm{in} \mathrm{the} \mathrm{middle} \mathrm{place} \end{gathered}$$

$\begin{array}{rcl} & & \mathrm{So} \mathrm{we} \mathrm{have} \mathrm{to} \mathrm{arrange} 4 \mathrm{telugu} \mathrm{books} \mathrm{keeping} \mathrm{hindi} \mathrm{in} \mathrm{the} \mathrm{middle} \mathrm{place}.\\ & & \end{array}$

$\begin{array}{rcl}\mathrm{No}.\mathrm{of} \mathrm{arrangements}& =& {}^7\mathrm{C}_4\times {}^4\mathrm{C}_1\times 4!\\ & =& \frac{7\times 6\times 5\times 4}{1\times 2\times 3\times 4}\times 4\times 4!\\ & =& \boxed{3360}\end{array}$