Given a set S, with n elements and given a whole number, k (kS is just a subset of S, with k elements where the order of the elements is not taken into account (two lists with the same elements in different orders are considered to be the same combination).

"My fruit juice is a combination of oranges, grapes and lemon"
We don't care what order the fruits are in, they could also be "grapes, oranges and lemon" or "lemon, oranges and grapes", its the same fruit juice.

The number of k-combinations (each of size k) from a set S with n elements (size n) is the binomial coefficient:

where n is the number of objects from which you can choose and k is the number to be chosen, and n! denotes the factorial.

Jose has 9 friends that he wants to invite to dinner but he can only invite six of them at one time. Out of the nine friends many different groups can he invite?

He can do 84 different invitations.

The 'The National Lottery' is a lottery game in which you have to deal with six whole numbers between 1 and 49. How many possible combinations of six numbers are there? If a combination of 6 numbers costs €1 how much would you have to pay in order to ensure that you have chosen the winning combination of numbers.

You have to wast €13,983,816 to be sure you have chosen the winning combination of numbers.

Enter any numbers n and k you want and the computer will calculate for you the number of combinations without repetition.