SOLUTION: An apartment complex offers apartments with four different options, designated by A through D. A = number of bedrooms (one through four) B = number of bathrooms (one through

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Question 1114853: An apartment complex offers apartments with four different options, designated by A through D.
A = number of bedrooms (one through four)
B = number of bathrooms (one through three)
C = floor (first through fifth)
D = outdoor additions (balcony or no balcony)
How many apartment options are available? Apply the Fundamental Counting Principle with two groups of items.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
4 choices for A.
3 choices for B.
5 choices for C.
2 choices for D.

total number of choices is 4 * 3 * 5 * 2 = 120


Answer by ikleyn(52815) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is a big  (a huge)  pitfall in this problem:



     Did you ever see one bedroom apartment with three bathrooms?



So, the pitfall in the given problem is that not all outcomes/options are independent.


Therefore, it would be not precisely correct in this case to apply the Fundamental Counting Principle by multiplying all options .


But the focus here is that the problem DOES NOT ask you apply the Fundamental Counting Principle to all categories of options at a time.


The problem asks you to apply it to only two groups of items.


You must select two categories/groups with independent outcomes.


For example, number of bedrooms, from one side, and the floor, from the other side, represent, probably, independent outcomes.


So, for this pair/(groups A and C) the number of apartment options is 4*5 = 20.

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The lesson to learn from my solution/discussion is THIS: 

   You may apply the Fundamental Counting Principle by multiplying options if and only if and only when these options/outcomes are independent.