An automobile manufacturer offers a station wagon with eithe

1. For 6 cylinders ( Manual or automatic), (with trailer hitch or not), for a total of 2*2=4
2. For 4 cylinders - Manual or automatic for a total of 2
3. Total number of possibilities is 4+2=6.

We are given that an automobile manufacturer offers a station wagon with the following:

1) 6-cylinder engine or 4-cylinder engine

2) manual transmission or automatic transmission

3) trailer hitch - only with a 6-cylinder engine.

We need to determine the number of possible combinations.

So, we have 2 possible scenarios:

Scenario #1:

6-cylinder engine (1 option)

manual or automatic transmission (2 options)

trailer hitch or no trailer hitch (2 options)

Thus, for scenario #1, there are 1 x 2 x 2 = 4 possible options.

Scenario #2:

4-cylinder engine (1 option)

manual or automatic transmission (2 options)

Thus, for scenario #2, there are 1 x 2 = 2 possible options.

The total number of combinations is 4 + 2 = 6.

Alternative solution:

By looking at the answer choices, we see that the largest number is 8. That means it won’t be more than 8 combinations. Therefore, we also could list out each combination.

Let’s use the following shorthand: 6c for 6-cylinder engine, 4c for 4-cylinder engine, m for manual transmission, a for automatic transmission, t for trailer hitch, and n for no trailer hitch. We have:

1) 6c-m-n
2) 6c-m-t
3) 6c-a-n
4) 6c-a-t
5) 4c-m-n
6) 4c-a-n

Recall that a trailer hitch can’t be on a station wagon with a 4-cylinder engine, so we can’t have 4c-m-t and 4c-a-t. Thus, there are only 6 combinations.

Answer: D

Possible Combinations:

6,M,H
6,M,N
6,A,H
6,A,N
4,M
4,A

Total = 6
ANSWER: D

Thanks for your explanation ScottTargetTestPrep!

But i always thought that in cases where order does not matter, we must divide the results in the end, for example in scenario 1 by 1*2*3 and in scenario 2 by 1*2, because we are dealing with a combination?

So why can we neglect that order does not matter in this question? I dont think we are dealing with a permutation here, since the question asks " How many combinations of the five options listed does the manufacturer offer for its station wagon?"

Thanks in advance!

Hi,

I dont really get what this mean "five options listed "?
The question is confusing indeed.
Why not how many combinations that the manufacturer could offer?
This question is not hard, but by saying 5 options listed, I could assume there is no 6-cylinder without trailer hitch. That's why I choose 4 )

The language in the question can be improved. However, the language is technically written in correct manner.

There are indeed five options offered: 6 cylinder, 4 cylinder, manual, auto, trailer.

6 cylinder model with either manual or auto transmission - This provides two combinations.

4 cylinder model with either manual or auto transmission - This provides two combinations.

6 cylinder model with trailer for both the models with manual or auto transmission - This provides two more combinations.

So, in total, we have six (6) combinations.

ANSWER: (D)

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