🎲 Combination Calculator (nCr)

ଏହି ଗଣନାକାରୀ ବିଷୟରେ

A combination counts how many ways you can choose r items from a set of n when order does not matter — picking the same group in a different sequence counts once. This calculator returns the exact count, the formula, and the matching number of ordered arrangements (nPr) for comparison.

The formula is nCr = n! / (r! × (n − r)!). For 10 items taken 3 at a time there are 120 distinct groups. Combinations are always smaller than permutations because each unordered group corresponds to r! different orderings, so nCr = nPr ÷ r!. Choosing none or all gives nC0 = nCn = 1, and as with permutations, r cannot exceed n.

Combinations answer "how many groups?" — the odds in a lottery, the number of possible five-card poker hands, ways to pick a committee, or terms in a binomial expansion. The value nCr is also called the binomial coefficient, the "n choose r" number in Pascal's triangle.