Question Video: Writing Combinations in Terms of Permutations | Nagwa Question Video: Writing Combinations in Terms of Permutations | Nagwa

# Question Video: Writing Combinations in Terms of Permutations Mathematics • Second Year of Secondary School

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Which of the following is equal to 41πΆ5? [A] 41π5/5! [B] 41π5/5 [C] 41π5 Γ 5! [D] 41π5 Γ 5

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### Video Transcript

Which of the following is equal to 41 πΆ five? Is it (A) 41 π five divided by five factorial, (B) 41 π five divided by five, (C) 41 π five multiplied by five factorial, or (D) 41 π five multiplied by five?

We begin by recalling our formulae for permutation and combination. The permutation πππ is equal to π factorial divided by π minus π factorial. And the combination ππΆπ is equal to π factorial divided by π minus π factorial multiplied by π factorial. Combining these two formulae, we see that ππΆπ is equal to πππ divided by π factorial. In this question, π is equal to 41 and π is equal to five. This means that 41 πΆ five is equal to 41 π five divided by five factorial. The correct answer is therefore option (A).

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