43. On a bookshelf, there are ten different books, three of which are on mathematics. In how many ways can all these books be arranged in a row so that the mathematics books are together?
43. Let's bind three mathematics books together so that they form a single book. Then we will have 8 books. They can be arranged in a row on a bookshelf in $8!=40320$ ways. Obviously, in each such arrangement, the mathematics books will continue to remain together if they are rearranged among themselves. This can be done in $3!=6$ ways. In total, we get $40320 \cdot 6=241920$ ways of the required arrangement of books on the shelf.