Ignoramus10431 wrote in
news
On 2015-07-12, Tim Wescott wrote:
On Sat, 11 Jul 2015 23:29:00 -0400, Steve Walker wrote:

Can't seem to figure out an answer. Permutation/combination stuff.
Suppose I have n red balls, x yellow balls, y green balls, and z orange
balls. (no blue. G) I need a formula for how many unique ways there
are to arrange them. Even better would be a formula for how many unique
ways to arrange them on the perimeter of a circle, so that no pattern
can be duplicated by rotating the circle. Extra credit for a link to an
algorithm to generate the patterns. Racking my brain, and Googling for
the last week.

If you had N = x + y + z unique balls*, then there would be N! (N
factorial) ways to arrange them. Within the yellow balls, there would be
x! unique ways to arrange them, but you lose that. Ditto green and
orange.

So there are

((x+y+z)!) / ((x!)(y!)(z!))

unique ways to arrange the balls in a line.

This is correct.

No, it's not. The OP has a total of K = n + x + y + z balls in *four* different colors.