Combinations & Permutations Calculator (nCr & nPr)
Combinations C(n,r)
0
Permutations P(n,r)
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Steps
Understanding Combinations and Permutations
Combinations count selections where order does not matter. Permutations count arrangements where order matters. C(n,r) = n!/(r!(n-r)!). P(n,r) = n!/(n-r)!.
Choosing 3 toppings from 10 is a combination (120 ways). Ranking 3 runners from 10 is a permutation (720 ways).
P(n,r) = C(n,r) x r! because each combination can be arranged in r! orders. Both are fundamental to probability and counting.
Frequently Asked Questions
Difference between combinations and permutations?
Combinations: order irrelevant. Permutations: order matters. P is always >= C.
What is factorial?
n! = product of all positive integers up to n. 5!=120. 0!=1.
How are combinations used in probability?
Lottery odds use combinations. Matching 6 from 49: 1/C(49,6)=1/13,983,816.
What is C(n,0)?
Always 1. There is exactly one way to choose nothing.