Combination Calculator (nCr)

This combination calculator works out nCr, the number of ways to choose r items from a set of n when the order of selection does not matter. Combinations are the right tool whenever you care which items end up in the group but not the sequence they were picked in. Working out how many six number Lotto tickets are possible, how many different five card hands can be dealt from a deck, or how many ways a panel of three can be selected from twelve applicants are all combination problems. The formula is n factorial divided by r factorial times the factorial of n minus r, which is the same as the permutation count nPr divided by r factorial, since dividing by r factorial removes all the different orderings of the same group. Combination totals grow quickly but more slowly than permutations, because order is no longer counted as different. The calculator works the result out using a stable step by step product rather than huge factorials, so it stays accurate for larger inputs and warns when an answer grows beyond the range it can display exactly. The simple test is whether reordering the chosen items gives you something genuinely different: if not, you want a combination. Enter your n and r values, with r no larger than n, to see the answer instantly.