Four mathematics books and seven history books are arranged on a bookshelf in how many of the possible arrangements are no two mathematics books next to each other?

120

Step-by-step explanation:

No of math books = 4

No of History books = 7

Since no two math books are next to each other, we can say each math book is sandwiched between two history books like

H⇔M⇔H

We can assume that this there books in system above is binded together, thus we will have

3 binded combinations H⇔M⇔H

1 single Math book M

1 single History book H

No of possible arrangements = (3+1+1) ! = 5! = 5 x 4 x 3 x 2 x 1 = 120