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Flip to reveal answersHow do you find n from ⁿP₂ = k?
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All 8 Flashcards — Find n from counting
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Question
How do you find n from ⁿP₂ = k?
Answer
ⁿP₂ = n(n − 1). Set n(n − 1) = k, rearrange to a quadratic, solve, and keep the positive whole-number root.
Question
How do you find n from ⁿC₂ = k?
Answer
ⁿC₂ = n(n − 1)/2. Multiply by 2 to get n(n − 1) = 2k, solve the quadratic, keep the positive root.
Question
Why reject the negative root when finding n?
Answer
n counts objects, so it must be a positive whole number — a negative root has no meaning.
Question
What does ⁿP₂ expand to?
Answer
n(n − 1).
Question
What does ⁿC₂ expand to?
Answer
n(n − 1)/2.
Question
Shortcut for ⁿCₐ = ⁿC_b when a ≠ b?
Answer
a + b = n, because ⁿCᵣ = ⁿCₙ₋ᵣ. e.g. ⁿC₃ = ⁿC₇ ⇒ n = 10.
Question
Solve ⁿP₂ = 42.
Answer
n(n − 1) = 42 ⇒ (n − 7)(n + 6) = 0 ⇒ n = 7.
Question
Solve ⁿC₂ = 28.
Answer
n(n − 1) = 56 ⇒ (n − 8)(n + 7) = 0 ⇒ n = 8.
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Full study notes for Find n from counting
Topic 1.10 hub
Counting & binomial (HL only)
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