00:01
On this problem, we are told that we have 12 marbles and five of them are black, three are red, two of them are white, and two of them are green.
00:27
And two green.
00:29
Now, we want to know how many different ways we can arrange these.
00:33
Now, this is just like the mississippi problem, just like the bookkeeper problem when you're arranging these in a line.
00:40
It's the same idea here.
00:42
So we have 12 marbles, and so if they were all different, there would be 12 factorial different ways to arrange them.
00:48
The thing is, though, they're not all different.
00:51
You have five black.
00:52
And so we divide by five factorial, because that'll cancel out the repeats here...