Question 5 • TN-Algebra II B SC 26-27 (For Credit)
Eli chooses two shirts from a group of five to pack for a weekend trip. Let each shirt be represented by A, B, C, D, and E. Which statements about the situation are true? Check all that apply.The combination of AB and BA are the same. Each shirt can be paired with any one of other the remaining shirts. There are twenty possible ways to choose the group of shirts. He has five choices for the first shirt and five choices for the second shirt. If he chooses shirt B, there are four possible outcomes for choosing the second shirt.
Answer
A
The combination of AB and BA are the same.
B
Each shirt can be paired with any one of other the remaining shirts.
C
There are twenty possible ways to choose the group of shirts.
D
He has five choices for the first shirt and five choices for the second shirt.
E
If he chooses shirt B, there are four possible outcomes for choosing the second shirt.
Explanation
The order of the shirts does not matter, so choosing A then B is the same group as choosing B then A. Each shirt can be matched with any of the other four shirts, so if Eli chooses B first, four shirts remain for the second choice. There are 10 distinct pairs altogether, not 20, and he does not have five choices for the second shirt after choosing the first.
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