00:01
So for this problem, to begin, we can find the probability that x equals 3 by taking the number of different possible ways to get a result of exactly 3.
00:11
Well, we know that the only possible way would be to get 1 -1 -1 -1.
00:15
So we have exactly one different or one possible way out of 216.
00:20
Then, to get x to be equal to 4, the only possible way would be to have 1 -1 -2 in any ordering.
00:30
That there are three different possible orderings.
00:34
So we'd have the probability that x equals four will be equal to three over 216.
00:43
To have x equals five, we need to have one, one, and three with three different possible ordering, so i'll say one, one, three times three, or one, two, two, with three possible orderings.
01:01
So we have that the probability that x equals five, comes out to 6 over 216.
01:10
To get that x equals 6, the different possible orderings would be to have 1 -1 and 4, or the different possible combinations would be 1 -1 and 4, which can occur three different ways.
01:25
Of course, when i say times 3, in this case, it's the idea of 1 -1 -3 -131 and 3 -1 -1 are equivalent results when we're considering the sum.
01:33
So we could have for x equals 6, 114, 141, 4 -1, 4 -1, 4 -1, 4 -1, 4 -1, or we could have one, two, three in each one of the possible orderings of one, two, and three together.
01:47
So there are six orderings of that.
01:49
Or we could have two to two, which only occurs one way.
01:53
So we would have the probability that x equals six, it's equal to three plus six is nine plus one gives us a result of ten over two hundred and sixteen.
02:02
Then x equals seven we have that the different possible ways or different possible combinations of results would be 1 1 and 5 with 3 different possible orderings one 2 and 4 with 6 different possible orderings 1 3 and 3 with 3 different possible orderings or we could have 2 2 and 3 with 3 different possible orderings so we have probability that x equals 7 will be equal to 15 over 216.
02:44
Then moving on to probability or to x equals 8, the different possible orderings would be 1 -1 -6 in three different ways.
02:55
1 -2 -5, which can be arranged in six different ways, 1 -3 -4, which occurs in six different ways, 2 -24, which can occur in three different ways, or 2 -33, which can occur in three different ways.
03:18
So we have the probability that x equals 8 would be equal to 21 over 21.
03:26
Moving on to x equals 9, we could have 3 -33, which can only happen one way.
03:38
We could have 2, 3, 3, 4, which can happen six different ways.
03:46
We could have one, three, and five, which can happen six different ways.
03:56
We could have, let's see here, other possible ways...