CalKit

Combination/Permutation Calculator

Calculate nCr combinations and nPr permutations.

조합 C(10, 3)
조합
120

풀이 과정

공식C(10, 3) = 10! / (3! × 7!)
1단계10! = 3,628,800
2단계3! = 6
3단계7! = 5,040
결과결과 = 120

Overview

The Combination/Permutation Calculator computes nCr (combinations) and nPr (permutations). Combinations count selections without regard to order, while permutations count arrangements where order matters. Essential for probability and counting problems.

Formula

Permutation: nPr = n! / (n - r)!

Combination: nCr = n! / (r! × (n - r)!)

Factorial: n! = n × (n-1) × (n-2) × ... × 2 × 1 (0! = 1)

Relationship: nCr = nPr / r!

How to Use

  1. 1Enter the total number of items n.
  2. 2Enter the number of items to choose r.
  3. 3Select either combination (nCr) or permutation (nPr).
  4. 4The result and calculation steps are displayed.

Tips

  • ✔Use permutations (P) when order matters, combinations (C) when it does not.
  • ✔Lottery odds use combinations: 45C6 = 8,145,060.
  • ✔nCr = nC(n-r), so if r > n/2, calculating with n-r is more efficient.

FAQ

Q. What is the difference between combinations and permutations in simple terms?

Choosing 3 people from 5 and assigning them as president, VP, and secretary is a permutation — order matters. Simply choosing 3 committee members from 5 is a combination — only the selection matters.

Q. What is a factorial (!)?

n! is the product of all natural numbers from 1 to n. For example, 5! = 5×4×3×2×1 = 120. By convention, 0! = 1.

Q. What are combinations and permutations with repetition?

These allow selecting the same item more than once. Permutations with repetition = n^r. Combinations with repetition = (n+r-1)Cr. For example, rolling 2 dice is 6² = 36 (permutation with repetition).

Related Calculators

Percentage Calculator

Calculate percentages, discounts, and rate of change.

Ratio Calculator

Simplify ratios and solve proportions.

Quadratic Equation Solver

Solve quadratic equations in the form ax² + bx + c = 0.

Fraction Calculator

Calculate fraction arithmetic and simplification.

GCD/LCM Calculator

Calculate greatest common divisor and least common multiple.

Standard Deviation Calculator

Calculate mean, variance, and standard deviation of data.