More Counting

[nami]

Hi. I have another problem I'm stuck on.

A, B, C, and D are nodes on a computer network. There are two paths between A and C, two between B and D, three between A and B and four between C and D. Along how many routes can a message from A to D be sent?

My so far approach: :idea:
I came up with two ways a message can go from A to D.

A to C, C to D --> 2 + 4 --> 6 paths
A to B, B to D --> 3 + 2 --> 5 paths

I'm thinking that the addition principle has to be applied here, since there is only one event. Am I making the right assumption? :?

 

[soroban]

Hello, nami!

A small (but significant) error . . .

A, B, C, and D are nodes on a computer network.
There are two paths between A and C, two between B and D, three between A and B
and four between C and D. .Along how many routes can a message from A to D be sent?

A to C, C to D \(\displaystyle \rightarrow\;\;2\,\times\,4 \:=\:8\) routes

A to B, B to D \(\displaystyle \rightarrow\;\;3\,\times\,2\:=\:6\) routes

. . Therefore, there are: \(\displaystyle \,8\,+\,6\:=\:14\) routes.

 

[nami]

Hi. Thanks so much!

I got confused, because I thought that the multiplication principle was used in the case that there are two events, and that the addition principle is used when there is only one outcome.

So, is it that going from A to C, then C to D is considered two events so you use the multiplication principle (the same for going A to B, then B to D). Since you only want the one outcome (going from A to D), you use the addition principle? :shock:

Wow, I think I just had an aha! moment. This stuff can be very confusing. Anyways, thanks again for your help!