An automobile manufacturer offers a station wagon with either a 6-cylinder engine or a 4-cylinder engine and with either a manual transmission or an automatic transmission. A trailer hitch is also offered, but only on a station wagon with a 6-cylinder engine. How many combinations of the five options listed does the manufacturer offer for its station wagon?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8


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Hi All,

Sometimes Combination Formula questions come with answers that are relatively small. In this prompt, we know that there are at least 3 options, but no more than 8 options. In these situations, it's usually pretty easy to "map out" all of the possible combinations, without having to do any special math.

We're told that a station wagon has a variety of 'traits':
1) Either a 6-cylinder engine or a 4-cylinder engine
2) Either a manual transmission or an automatic transmission
3) A trailer hitch (but ONLY on a 6-cylinder engine)

We're asked for the number of different combinations of traits on a station wagon. We can list them out:

6 cyl and manual
6 cyl and manual and hitch
6 cyl and automatic
6 cyl and automatic and hitch
4 cyl and manual
4 cyl and automatic

Total combinations = 6

Final Answer:

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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
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