| | | | | |N|N|N|N| |M|M|M|M|M|O|O|O|O| |A|A|A|A|A|V|V|V|V| |T|T|T|T|T|E|E|E|E| |H|H|H|H|H|L|L|L|L| For the above way of placing the books, there are 5! ways to arranging the math books, and for each of those ways there are 4! ways of arranging the novels. That's 5!4! ways for having all 5 math books on the left and all four novels on the right. |N| | | | | |N|N|N| |O|M|M|M|M|M|O|O|O| |V|A|A|A|A|A|V|V|V| |E|T|T|T|T|T|E|E|E| |L|H|H|H|H|H|L|L|L| For the above way of placing the books, there are 5! ways to arranging the math books, and for each of those ways there are 4! ways of arranging the novels. That's 5!4! ways for having 1 novel on the left, then the 5 math books, then 4 novels on the right. |N|N| | | | | |N|N| |O|O|M|M|M|M|M|O|O| |V|V|A|A|A|A|A|V|V| |E|E|T|T|T|T|T|E|E| |L|L|H|H|H|H|H|L|L| For the above way of placing the books, there are 5! ways to arranging the math books, and for each of those ways there are 4! ways of arranging the novels. That's 5!4! ways for having 2 novels on the left, then the 5 math books, then 2 novels on the right. |N|N|N| | | | | |N| |O|O|O|M|M|M|M|M|O| |V|V|V|A|A|A|A|A|V| |E|E|E|T|T|T|T|T|E| |L|L|L|H|H|H|H|H|L| For the above way of placing the books, there are 5! ways to arranging the math books, and for each of those ways there are 4! ways of arranging the novels. That's 5!4! ways for having 3 novels on the left, then the 5 math books, then 1 novels on the right. |N|N|N|N| | | | | | |O|O|O|O|M|M|M|M|M| |V|V|V|V|A|A|A|A|A| |E|E|E|E|T|T|T|T|T| |L|L|L|L|H|H|H|H|H| For the above way of placing the books, there are 5! ways to arranging the math books, and for each of those ways there are 4! ways of arranging the novels. That's 5!4! ways for having all four novels on the left and all five math books on the right. That's a total of 5*5!*4! = 14400 Edwin