Question

John has 4 math books, 6 biology books and 8 statistic books to arrange on a shelf. In how many ways can he arrange the books so that books on the same subject are grouped together?

Answer 1

Considering the 4 math books, there are 4 possible positions for the first book selected. Having placed the first book, there are 3 possible positions for the second book selected, 2 possible positions for the third book selected and only 1 position for the fourth book selected. This gives a total of 4 * 3 * 2 * 1= 4! possible arrangements for the math books.
Similarly there are 6! possible arrangement for the 6 biology books and 8! possible arrangements for the statistic books.
Finally there are 3! possible arrangement for the 3 groups of books. So the total number of possible arrangements is given by:
\[\large 3! \times 4! \times 6! \times 8!=you\ can\ calculate\]

Answer 2

Thanks!

Answer 3

You're welcome :)