Combination & Permutation Calculator
nCr and nPr, instantly · 조합·순열 계산기
Enter n (total items) and r (chosen) to get both the combination C(n, r) and permutation P(n, r).
How to use this calculator
- Enter n — the total number of items to choose from.
- Enter r — how many you select (0 ≤ r ≤ n).
- Press Calculate to see C(n, r) and P(n, r) together.
n(전체 개수)과 r(고르는 개수, 0 ≤ r ≤ n)을 입력하고 Calculate를 누르면 조합 C(n, r)과 순열 P(n, r)이 함께 나옵니다.
Combinations vs permutations
The deciding question is "does order matter?" A permutation counts ordered arrangements, P(n, r) = n!/(n − r)!; a combination counts unordered selections, C(n, r) = n!/(r!(n − r)!). They are linked by C(n, r) = P(n, r)/r!. For the full derivations see combinations, permutations, and counting principles.
판단 기준은 "순서가 중요한가?"입니다. 순열 P(n, r) = n!/(n − r)!은 순서 있는 배열, 조합 C(n, r) = n!/(r!(n − r)!)은 순서 없는 선택이며, C(n, r) = P(n, r)/r! 관계입니다. 자세한 내용은 조합·순열·경우의 수 문서를 참고하세요.
Worked example
Choosing 3 from 5: P(5, 3) = 5 · 4 · 3 = 60 ordered arrangements, and C(5, 3) = 60 / 3! = 10 unordered selections. A larger one: the number of 5-card poker hands is C(52, 5) = 2,598,960.
5개 중 3개: P(5, 3) = 5·4·3 = 60(순서 있음), C(5, 3) = 60/3! = 10(순서 없음). 더 큰 예로 5장 포커 패는 C(52, 5) = 2,598,960입니다.
Frequently asked questions
What is the difference between nCr and nPr? nPr (permutations) counts ordered arrangements; nCr (combinations) counts unordered selections. nPr is always r! times nCr.
What are the formulas? P(n, r) = n!/(n − r)! and C(n, r) = n!/(r!(n − r)!).
When do I use combinations? When the order of selection does not matter — a committee, a hand of cards, a subset.
nPr(순열)은 순서 있는 배열, nCr(조합)은 순서 없는 선택이며 nPr = r!·nCr입니다. P(n, r) = n!/(n − r)!, C(n, r) = n!/(r!(n − r)!). 순서가 무관하면(위원회·카드 패·부분집합) 조합을 씁니다.
Keep practicing
Drill counting on C:Stat, read the combinations and permutations guides, or browse more tools on the calculators hub.