The COMBINATIONS (nCk) calculator computes the number of combination possible in a set of k elements containing exactly one of each unique element from a finite set of n objects where order does not matter.
INSTRUCTIONS: Enter the following:
Combinations (nCk): The calculator computes and return the number of combinations. Combinations also plays the core role in the Binomial Coefficient and in the construction of Pascal's Triangle.
The combination equation computes the number of possible combinations of k elements (unique sets) from within the set of n objects. Unlike permutations, the order of the distinct selected items are not considered in the set of combinations. We denote the number of combinations as C(n,k). The number C(n,k) or `C_"(n,k)"` is the the probability of choosing one specific set of k elements from a set of n-objects.
The formula for the number of combinations is as follows:
nCk = ` (n!)/(k!(n-k)!)`
where:
This equations can be used to answer a question like: How many different hands can be dealt in a 5 card Poker deal.
The answer is: 52! / ( 5! ( 52-5)! ) = 2598960
So, from a set of 52 cards, there are 2,598,960 possible different hands that could be dealt.
Another example would be the number of combinations of players on the field from a 50 player football team where every player can play any position on both offense or defense. Since each player is a unique person and the number of players on the field is eleven, the number of possible player combinations would be:
C(50,11) = 50! / ( 11! (50-11)! ) = 37,353,738,800