Question

John has 4 math books, 6 biology books and 8 statistics 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

so, what are your ideas? what do you think you need to use?

Answer 2

One way to group by subject is math, then bio, then stats (though wouldn't these technically fall under math?). Another is by bio, then math, then stats. And so on, giving 3! = 6 ways to arrange the groups (distinctly, meaning bio-math-stats is different from from math-bio-stats, and so on).

For the books themselves: Within the math category, you have 4! = 24; bio, you have 6! = 720; and stats, you have 8! = 40320 ways.

For a sequence of books, you then have \(4!6!8!\) to arrange on a shelf, times 3! to account for the different grouping arrangements.

Answer 3

Great idea! Thanks! :)