Let's analyze each statement one by one:
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The combination of AB and BA are the same.
- True. In combinations, the order does not matter, so selecting shirt A and shirt B is the same as selecting shirt B and shirt A.
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Each shirt can be paired with any one of the remaining shirts.
- True. Each shirt can be paired with any of the other four shirts. For example, if shirt A is chosen, it can be paired with B, C, D, or E.
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There are twenty possible ways to choose the group of shirts.
- False. The number of ways to choose 2 shirts from a group of 5 is calculated using combinations (not permutations) as follows: \[ \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10. \] Therefore, there are 10 possible combinations, not 20.
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He has five choices for the first shirt and five choices for the second shirt.
- False. When choosing a shirt for the second choice, he only has 4 options left (the 5th shirt has already been chosen). Thus, while he has 5 choices for the first shirt, he does not have 5 choices for the second.
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If he chooses shirt B, there are four possible outcomes for choosing the second shirt.
- True. If shirt B is chosen first, the remaining shirts available for the second choice are A, C, D, or E, which gives him 4 options.
In summary, the true statements are:
- The combination of AB and BA are the same.
- Each shirt can be paired with any one of the remaining shirts.
- If he chooses shirt B, there are four possible outcomes for choosing the second shirt.
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