I agree with your answer. Think about it.
The given answer just makes no sense!
What is the probability a random journey from A to B passes through the point D? You can only move right or up.
I got 10 ways from A to D and 5 ways from D to B. I also got 210 ways from A to B.
Then
The anwers give please help with what I did wrong!
This is a little lat but here is my solution.
First, I am not sure if you know the premutation formula for multiple objects. For example, how many different words can you form with that is simply . But what if I have then the formula is .
In general let there be a words consisting of of or of , ... of then the number of possible arrangements possible is .
The above formula is what we will use here. Now in order to go from A to B we need to go 6 times to the right and 4 times up. Thus, we can think of a path as an -pule. So for example, represents 6 times to the right and 4 times up in that order. So the question is to determine how many 10-tuples can we form were we use (right) 6 times and (up) 4 times. That is .
Now you need to count the path from A to D and from D to B and multiple there results together to give you the number of path passing through D. That is, .
Thus, the probability is .
If you are interested in my Real Multidimensional Analysis class we introduced something called "multi-index notation".
For a vector we define and where are non-negative integers. And for a vector we define .
So we can write,
.
(Where means all ways of getting components to add up to .)