00:01
So in this question here, in the first part, we are going to consider that how many ways, paths, can we have so that we reach the top row here.
00:10
And we need to consider the number of paths that we are going to get to that top row for each one of those positions, like five positions that we have.
00:21
So in item a, we are considering that the soccer ball can only, in this case, i'm going to say walk, one square at a time.
00:30
Or move one square at a time we also have that it can move diagonally left to the row above or diagonally right to the row above so in this case for the first consider the start position we have one way of coming this way or one way you'll come this way then to go to this position here if you are here you have one if you are here you have others so in this case you have two ways of get into that position for this one we only have one way which is going coming from this one and that this one is the same one then we need to consider this here because it is always moving uh diagonally here so in this case for this one here we have three positions because for the previous um or three possible paths because for the previous row here the the two two possible ways in which we can get to this point.
01:33
We have already one path, and for this one we have two.
01:37
So this means that to get here, we have three possible.
01:40
The same thing still for this one.
01:42
Then, because we cannot go like up ahead here, straight up to the row above, we have zero and zero for this.
01:52
For this diagonal here, now we consider that to get here, we are considering the path that got us up to this point.
02:00
So in this case we have three total.
02:03
For this one here we have to consider that we are either here or here, which let us with like six possible paths here, three for each side, and for the last one we have only three possible paths...