What is the binomial coefficient 'n choose k' for n = 7, k = 3?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

What is the binomial coefficient 'n choose k' for n = 7, k = 3?

Explanation:
This question tests how many ways you can choose a subset of a given size from a larger set, using the binomial coefficient n choose k. It’s computed with the formula n! / (k!(n−k)!). For n = 7 and k = 3, that becomes 7! / (3!4!). Simplifying, (7×6×5) / (3×2×1) = 35. So there are 35 different 3-item groups you can form from seven items. The other numbers correspond to choosing a different number of items (like 7 for choosing 1 item, 21 for choosing 2 items), or to ordered arrangements rather than unordered subsets.

This question tests how many ways you can choose a subset of a given size from a larger set, using the binomial coefficient n choose k. It’s computed with the formula n! / (k!(n−k)!). For n = 7 and k = 3, that becomes 7! / (3!4!). Simplifying, (7×6×5) / (3×2×1) = 35. So there are 35 different 3-item groups you can form from seven items. The other numbers correspond to choosing a different number of items (like 7 for choosing 1 item, 21 for choosing 2 items), or to ordered arrangements rather than unordered subsets.

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