00:01
Okay, suppose that three die are rolled.
00:03
So one outcome could be one, one, one, one, one, two, one, one, three, one, two, one, and so on and so forth.
00:13
Okay, so how many different outcomes? well, in the first die, there's six outcomes, in the second, there's six, in the third, there's six, and these are all independent.
00:22
So about the fundamental counting principle, six times six times six, there's a total of 216 outcomes.
00:30
So what am i trying to find here? so first let's find how many ways a sum of six can be obtained.
00:37
Okay, so how could i add to six? well, i could do one, one, four, and this could be mixed up as well, one, four, one, or four, one, one.
00:48
Okay, there's three different ways to do that.
00:50
What else could i do? i could do one, two, and then three.
00:54
This could be two, one, three, or this could be one, three, two, or this could be two, three, one.
01:07
Okay, so that's six.
01:08
What else could i do? well, i could do one and then a three, and then this would have to be a two, which i already have, so i don't need to double count that.
01:19
Okay, what about one and a four? i could do one and a four and then a one...