Work out the number of combinations or permutations when choosing k out of n elements.
For combinations, where order doesn't matter, the notation is:
Example: "How many ways can you choose 3 out of 10 people for a team?" — here it doesn't matter what order the 3 are chosen in, so you use combinations.
For permutations, where order matters, you instead use:
Example: "How many ways can 3 out of 10 people finish 1st, 2nd and 3rd?" — here the order matters completely, so you use permutations.
With combinations, order doesn't matter (choosing A, B, C is the same as B, C, A), while with permutations, order counts as different outcomes. Permutations therefore always give an equal or greater count than combinations for the same n and k.
Because the number of possibilities grows very quickly with n and k — this is called combinatorial explosion. The calculator uses a method that avoids computing factorials directly, so it can handle large numbers without breaking.
Combinatorics is used, among other things, to work out probabilities in lotteries and card games, the number of possible passwords, or the number of ways to organize a group of people.