Question Video: Writing Combinations in Terms of Permutations Mathematics

Which of the following is equal to 41𝐢5? [A] 41𝑃5/5! [B] 41𝑃5/5 [C] 41𝑃5 Γ— 5! [D] 41𝑃5 Γ— 5

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Video Transcript

Which of the following is equal to 41 𝐢 five? Is it (A) 41 𝑃 five divided by five factorial, (B) 41 𝑃 five divided by five, (C) 41 𝑃 five multiplied by five factorial, or (D) 41 𝑃 five multiplied by five?

We begin by recalling our formulae for permutation and combination. The permutation π‘›π‘ƒπ‘˜ is equal to 𝑛 factorial divided by 𝑛 minus π‘˜ factorial. And the combination π‘›πΆπ‘˜ is equal to 𝑛 factorial divided by 𝑛 minus π‘˜ factorial multiplied by π‘˜ factorial. Combining these two formulae, we see that π‘›πΆπ‘˜ is equal to π‘›π‘ƒπ‘˜ divided by π‘˜ factorial. In this question, 𝑛 is equal to 41 and π‘˜ is equal to five. This means that 41 𝐢 five is equal to 41 𝑃 five divided by five factorial. The correct answer is therefore option (A).

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