Explanation

Starting with choice (A), there are 3 slots on the team, with 5 experienced engineers available for the first slot, 4 for the second slot, and 3 for the third slot. Order doesn’t matter, so divide by 3! to get \(\frac{5 \times 4 \times 3}{3 \times 2 \times 1}= 10\). Choice (A) is correct.

For choice (B), you have 3 apprentice engineers available for 2 slots and once again, order doesn’t matter. \(\frac{3 \times 2}{2 \times 1}= 3\). Choice (B) is correct and you can eliminate choice (C), which contradicts choice (B).


For choice (D) you have \(\frac{5 \times 4}{1 \times 2}= 10\), so choice (D) is correct.

Choice (E) is incorrect because \(\frac{5 \times 4 \times 3 \times 2}{4 \times 3 \times 2 \times 1}= 5\). The correct answers are choices (A), (B), and (D).
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Sandy
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