Expand, then solve a quadratic: ⁿP₂ means n(n − 1). Set it equal to the number, multiply out, and solve the quadratic — then keep only the root that makes sense (n must be a positive whole number).
IB-style question — find n from ⁿP₂
Solve ⁿP₂ = 42 for n.
Step by step
- Expand the permutation.
- Set equal to 42 and rearrange to a quadratic.
- Factorise.
- n must be a positive whole number, so reject n = −6.
Final answer
n = 7.
ⁿP₂ = n(n − 1): set n(n − 1) = 42, solve the quadratic, n = 7.
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Same plan, clear the fraction first: ⁿC₂ means n(n − 1)/2. Set it equal, multiply by 2 to clear the fraction, then solve the quadratic and keep the sensible root.
IB-style question — find n from ⁿC₂
Solve ⁿC₂ = 28 for n.
Step by step
- Expand the combination.
- Set equal to 28 and multiply both sides by 2.
- Rearrange and factorise.
- Keep the positive whole-number root.
Final answer
n = 8.