ExplanationThis problem involves permutations, because the order matters since the ties are all distinct. Start with Paul wearing a red tie. He has 3 red tie choices and Allen has 2 remaining red tie choices, giving them a product of 6 permutations.

For green ties, they have 5 × 4 = 20 permutations. For blue ties, they have 6 × 5 = 30 permutations.

The grand total is 56 permutations.

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Sandy

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