fozzzy wrote:
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
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
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