Calculate combinations C(n,r) - the number of ways to select r items from n items where order doesn't matter. With or without repetition.
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Calculate combinations instantly with our easy-to-use calculator. Find the number of ways to select r items from n items where order doesn't matter. Perfect for probability, statistics, and lottery calculations.
A combination is a selection of items where the order doesn't matter. C(n,r) represents the number of ways to choose r items from a set of n items. For example, selecting 3 students from a class of 20 for a committee - the group (A,B,C) is the same as (C,B,A). Without repetition: C(n,r) = n!/(r!(n-r)!). With repetition: C(n+r-1,r).
Combination Formula
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Calculate combinations with or without repetition
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In combinations, order doesn't matter (ABC = BAC). In permutations, order matters (ABC ≠ BAC). Use combinations when selecting a group, like choosing team members. Use permutations when arranging in order.
Use combination with repetition when items can be selected multiple times and order doesn't matter. For example, selecting 3 scoops of ice cream from 5 flavors where you can pick the same flavor multiple times.
For a lottery like 6/49 (pick 6 from 49), use C(49,6) = 49!/(6!×43!) = 13,983,816. This means there are about 14 million possible combinations, giving you a 1 in 14 million chance.