Calculate nPr and nCr instantly — with step-by-step formulas
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Step-by-step breakdown
Factorial values
Permutation (order matters)
P(n, r) = n! / (n − r)!
= 10! / 7!
= 720
Combination (order doesn't matter)
C(n, r) = n! / (r! × (n − r)!)
= 10! / (3! × 7!)
= 120
Tip: nPr is always ≥ nCr because permutations count each combination's arrangements separately. nPr = nCr × r!
Quick Examples
Formulas & Definitions
A permutation and combination calculator computes two fundamental results in combinatorics: nPr, the number of ordered arrangements of r items chosen from n, and nCr, the number of unordered selections. Whether you are solving a probability problem, calculating lottery odds, or working through a statistics exam, this tool delivers exact answers with a full formula breakdown in seconds.
A permutation (nPr) counts arrangements where order matters — picking A then B is different from B then A. A combination (nCr) counts selections where order does not matter — {A, B} and {B, A} are the same group. This is why nPr is always greater than or equal to nCr for any given n and r.
Permutations: P(n, r) = n! / (n − r)!. Combinations: C(n, r) = n! / (r! × (n − r)!). Both rely on factorials, where n! means multiplying all positive integers from 1 up to n together.
r represents how many items you select from a pool of n items. You cannot choose more items than exist in the pool, so r must always be less than or equal to n. The calculator will flag this as an error if r exceeds n.
For a 6/49 lottery, set n = 49 (total balls) and r = 6 (balls drawn). The combination C(49, 6) gives the total number of possible tickets — about 13,983,816. Since the draw order doesn't matter, you use nCr, not nPr.