Permutations & Combinations
Combinatorics, Algebra
Intro: Choose ordered (permutations) or unordered (combinations) selections.
Worked example
- n=10, r=3
- Goal: compute $^{n}P_r$ and $^{n}C_r$.
- Inputs: $n=10$, $r=3$.
- Permutations: $^{10}P_3=\dfrac{10!}{7!}=10\cdot9\cdot8=720$.
- Combinations: $^{10}C_3=\dfrac{10!}{3!7!}=\dfrac{10\cdot9\cdot8}{3\cdot2\cdot1}=120$.
- Answer: $\boxed{{}^{10}P_{3}=720,\; {}^{10}C_{3}=120}.$
FAQs
Allow repetition?
This basic tool assumes no repetition. A variant with repetition can be added if needed.
Why choose Mathix?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.