Permutation & Combination Calculator
Count arrangements and selections (nPr and nCr).
Combinations — nCr
120
order doesn't matter
Permutations — nPr
720
n!
3,628,800
Order is the whole question
Picking 3 of 10 people for distinct roles (president, VP, treasurer) is a permutation: 10×9×8 = 720 ways. Picking 3 for an equal committee is a combination: 720 ÷ 3! = 120, because each trio was counted in every internal order.
Where these show up
Combinations price lottery odds (6 of 49: about 1 in 14 million), poker hands, and A/B test groupings; permutations count passwords and rankings. The factorials explode fast — that growth is exactly why brute-forcing ordered arrangements fails early.
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