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A real estate agent has 4 homes for sale: [tex]$A, B, C$[/tex], and [tex]$D$[/tex]. Here are the listing prices:

- Home A: [tex]$\$[/tex]150,000[tex]$
- Home B: $[/tex]\[tex]$250,000$[/tex]
- Home C: [tex]$\$[/tex]190,000[tex]$
- Home D: $[/tex]\[tex]$550,000$[/tex]

The agent wants to randomly select 2 of the 4 homes to show in an open house this coming weekend. Which of the following gives a complete list of all possible samples of size 2 selected from this population of 4 homes without replacement?

A. [tex]$AB, CD$[/tex]

B. [tex]$A, B, C, D$[/tex]

C. [tex]$AB, AC, AD, BC, BD, CD$[/tex]

D. [tex]$AA, AB, AC, AD, BB, BC, BD, CC, CD$[/tex]



Answer :

GinnyAnswer
To determine the complete list of all possible samples of size 2 selected from a population of 4 homes without replacement, we need to consider the combinations of the homes taken two at a time.

Given homes are: A, B, C, and D.

We want to select pairs without replacement, meaning once a home is selected, it is not included again in the selection.

A combination means that the order of selection does not matter. Therefore, we need to list all unique pairs (i.e., AB is the same as BA).

Here are all the possible pairs:
1. Pair A and B: (A, B)
2. Pair A and C: (A, C)
3. Pair A and D: (A, D)
4. Pair B and C: (B, C)
5. Pair B and D: (B, D)
6. Pair C and D: (C, D)

So, the complete list of all possible samples of size 2 selected from the 4 homes without replacement is as follows:
- (A, B)
- (A, C)
- (A, D)
- (B, C)
- (B, D)
- (C, D)

Therefore, the correct answer is:
[tex]\[ A B, A C, A D, B C, B D, C D \][/tex]

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