There are five distinct computer science books, three distinct mathematics
books, and two distinct art books. In how many ways can these
books be arranged on a shelf if no two of the three mathematics books
are together?
I am getting $3507840$ by doing 10! - (3*8!). Is it correct?
Best Answer
Arrange the non-maths books, $7!$ ways. There are now $8$ gaps between books (including a "gap" at each end of the row). Choose one of these gaps for the first maths book, a different gap for the second and a different gap for the third.
Answer: $7!\times8\times7\times6$.