if there were ten boys to line up on a bench, then it should be 10! ways of arranging them.
but two of those boys are bosom buddies so they gotta stick together as a unit. so we count them as a unit (who are we to prohibit homosexuality?). so in fact, there's 9 units to arrange. that's 9! ways of arrangement.
now 9! is not the answer because we still gotta arrange our bosom buddies... consider this:
for every arrangement there is a version:
..... A B......
......B A......
where A and B are the bosom buddies and the dotties represent all other ppl in the 9! possible arrangements. so in fact, there's two of 9! to consider...
so the answer, by multiplication rule, is 2! x 9!
but two of those boys are bosom buddies so they gotta stick together as a unit. so we count them as a unit (who are we to prohibit homosexuality?). so in fact, there's 9 units to arrange. that's 9! ways of arrangement.
now 9! is not the answer because we still gotta arrange our bosom buddies... consider this:
for every arrangement there is a version:
..... A B......
......B A......
where A and B are the bosom buddies and the dotties represent all other ppl in the 9! possible arrangements. so in fact, there's two of 9! to consider...
so the answer, by multiplication rule, is 2! x 9!
