Question 1083526: suppose that a personal computer system contains choices petaining to memory size (4 sizes), hard disc size (3 sizes), monitor size (2 sizes), and printer type (2 types, the number of different "systems" can be computed from
4*3*2*2
(4*3)/(2*2)
4!3!2!2!
4!3!2!2!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Answer: Choice A) 4*3*2*2
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Explanation:
Using the counting principle, we simply multiply out all of the choices (4,3,2 and 2) for each of the types of items we pick. This is assuming we pick exactly one type of each item only. Another assumption is that each choice is independent from the others.
So we'll have 4*3*2*2 = 12*2*2 = 24*2 = 48 different computer configurations.
It looks like your teacher doesn't want you to actually compute the expression so leave it as 4*3*2*2, which is why the answer is choice A.
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Extra Information (this section is optional):
This is what the tree would look like
(Image generated by GeoGebra which is free graphing software).
- The four blue nodes represent the different memory choices. We can denote them as the set {M1,M2,M3,M4}
- Under each blue node is a set of three red nodes, representing the different hard drive choices. We can denote them as the set {H1,H2,H3}
- Under each red node is a set of 2 green nodes, representing the different monitor sizes. We can denote them as the set {D1,D2} (D for display).
- Under each green node is a set of 2 purple nodes, representing the different printer types. We can denote them as the set {P1,P2}
If you counted out all of the purple nodes, then you'd count out 48 of them in total. Counting this many nodes is tedious. Luckily the pattern of the nodes allows us to multiply the values. It's no coincidence that 4*3*2*2 = 48 and there are 48 purple nodes.
Each printer node at the bottom is the result of following a specific path.
One such path is highlighted in yellow (below)
that path is the result of picking memory M2, hard drive H3, monitor type D2 and printer type P1. This unique path is one of 48 total.
Note: normally I would label the drawing nodes but there are so many of them that I decided to leave the labels out.
Another Note: I recommend looking at the article link I posted for the counting principle. It shows a much simpler table from a simpler example.
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