In how many ways can 4 books of mathematics and 3 books of english can be placed on a shell so that books on the same subject always remain together?

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Solution

There are two possible cases that either Maths books are placed on left and English books are placed on right or vice versa.
Total arrangements of placing Maths books $= 4! = 24$
Total arrangements of placing English books $= 3! = 6$

So, total possible ways that books of the same subject always remain together $= 2 \times 24 \times 6 = 288$

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