Hi. The question is:
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 thinking:
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
Do I use the addition or multiplication principle for this problem?
Thanks!
A to C ,C to D ==> (2)x(4)ways=8 ways
A to B ,B to D = 3x2 =6 ways
Since both events are mutually exclusive then we using sum rule= 8 + 6 =14
Well, let me put on my clown shoes and try to answer that for you!
In this case, you want to find the total number of routes from A to D. It seems you have correctly identified the two possible ways: A to C, C to D and A to B, B to D.
Now, the addition principle wouldn't be suitable here because you are looking for the total number of routes, not the number of individual pathways.
To get the total number of routes, you need to apply the multiplication principle. This principle states that if there are n ways to do something and m ways to do another thing, then the total number of ways to do both is n * m.
So, in your case, you have 2 routes from A to C and 4 routes from C to D. Applying the multiplication principle, the total number of routes from A to D would be 2 * 4, which gives you a total of 8 routes.
So, there you have it! You can take 8 different routes from A to D. Now, let's hope none of them involve a detour through the circus!
To find the total number of routes from A to D, you need to use the multiplication principle because the arrangement of paths matters.
You correctly identified two paths: A to C, C to D, and A to B, B to D.
To find the number of routes for each path, multiply the number of paths available for each step.
For the A to C, C to D path:
There are 2 paths from A to C and 4 paths from C to D.
So, the total number of routes for this path is 2 * 4 = 8.
For the A to B, B to D path:
There are 3 paths from A to B and 2 paths from B to D.
So, the total number of routes for this path is 3 * 2 = 6.
Finally, to find the total number of routes from A to D, you add the number of routes for each individual path: 8 + 6 = 14 paths.
Therefore, a message from A to D can be sent along 14 routes.
To solve this problem, you will use the multiplication principle, which states that if there are m ways to do one thing and n ways to do another thing, then there are m * n ways to do both things.
In this case, you have two paths from A to C and four paths from C to D. By the multiplication principle, there are 2 * 4 = 8 ways to go from A to C and then from C to D.
Similarly, you have three paths from A to B and two paths from B to D. Applying the multiplication principle, there are 3 * 2 = 6 ways to go from A to B and then from B to D.
Therefore, there are a total of 8 + 6 = 14 different routes that a message can be sent from A to D.