There are four topics, considering the dictionary as a "topic"
{Math Books, English books, Science books, Dictionary}
and 4 positions for them on the shelf,
{leftmost, next to left, next to right, rightmost}
So there are 4! ways to order the topics.
Within each of these 4! orderings of the topics, there are
3! ways to arrange the Mathematics books,
5! ways to arrange the English books,
4! ways to arrange the Science books, and
1! way to "arrange" the dictionary.
Answer 4!3!5!4!1! = 24*6*128*24*1 = 414720.
Edwin
