There are seven positions to keep three English books and four Math books, out of which on position $1$ and $4$ we can only place Math and English books, respectively.
Since, available positions are five, we’ve to choose three of them to keep Math books and two of them to keep English books. This can be done in ${5 \choose 3} \times {2 \choose 2}$ ways.
Now, we’ve four positions selected for Math books, we can place Math books in those positions in ${6 \choose 4} \times 4!$ ways.
We also have three positions selected for English books, we can place English books in those positions in ${5 \choose 3} \times 3!$ ways.
Finally, number of ways to arrange books on shelf $= \{ {5 \choose 3} \times {2 \choose 2} \} \times \{ {6 \choose 4} \times 4! \} \times \{ {5 \choose 3} \times 3! \} = \{ 10 \times 1 \} \times \{ 15 \times 24 \} \times \{ 10 \times 6 \} = 216000$
Answer :- A.
