Calculate the number of permutations (nPr), the number of ways to arrange r items chosen from a set of n distinct items, where order matters.
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nPr = n! ÷ (n − r)!, the number of ways to select and arrange r items from a set of n distinct items, where the order of selection matters. For example, arranging 3 runners in 1st, 2nd and 3rd place out of 10 competitors gives 10P3 = 10 × 9 × 8 = 720 possible orderings.
The key distinction is whether order matters: permutations count arrangements (1st-2nd-3rd place is different from 2nd-1st-3rd), while combinations count selections regardless of order (a committee of 3 people is the same group no matter what order they were chosen in). Our Combination Calculator handles the order-doesn't-matter case.
It means swapping the position of two selected items creates a genuinely different outcome, like assigning gold, silver and bronze medals, versus just picking any 3 people for a team where their order of selection is irrelevant.
Then nPr simply equals n! (n factorial), the number of ways to arrange all n items in some order.
No, you can't arrange more items than exist in the set, so r must be less than or equal to n.
Combination Calculator
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