00:01
All right, so the question is asking for all the distinguishable permutations of a, a, a, b, c.
00:12
Now, let's assume for a second that we are looking instead at distinguishable a's, distinguishable b's, and distinguishable c's.
00:22
So let's say a1, a2, a3, and then b1, b2, and then b2, and then c1.
00:36
So since in this question, there are going to be six distinguished characters, distinguishable characters, i should say.
00:44
There are going to be six factorial arrangements because arranging n different characters is going to be n factorial possibilities.
00:54
But we have to remember that we cannot actually see these labels.
01:00
So to us, a1, a2, a3 is going to look, identical as a1, a3, a2, or a3, a1, et cetera, et cetera.
01:19
In fact, there are three factorial or six permutations that are going to seem identical to us, even if they are different.
01:27
So it can be a1, a2, a3, a1, a3, a2, a2, a2, a2, a2, a2, a2, a2, a1a3, a2, a2, a2, a2, a2, a2, a2, take into account all the different permutations of a.
01:53
And then similarly, for b, we don't know whether it's going to be b1, b2, or b2, or b2...