In how many ways 4 books on Mathematics and 3 books on English be placed on a Shelf so that books of the same subject always remain together?
for the position of mathematics books and English books, there are two possibilities.
either Maths books are placed on left side and English books are placed on the right side or vice versa. i.e. 2 ways
now 4 mathematics books can be arranged in 4! ways i.e. 4*3*2 = 24 ways
and 3 English books can be arranged in 3! ways = 3*2 = 6 ways
total number of ways of arrangement = 2*4! *3!
=2*24*6
= 288 ways
hope this helps you
either Maths books are placed on left side and English books are placed on the right side or vice versa. i.e. 2 ways
now 4 mathematics books can be arranged in 4! ways i.e. 4*3*2 = 24 ways
and 3 English books can be arranged in 3! ways = 3*2 = 6 ways
total number of ways of arrangement = 2*4! *3!
=2*24*6
= 288 ways
hope this helps you