c(n, k) = number of subsets size k in a set of size n.

     c(n, 0) = 1
     c(n, 1) = n
     c(n, n) = 1

     c(n, k) = c(n, n - k)  

     say our set is {1, 2, 3, .... n}

     there are two types of subsets:
        subsets INCLUDING 1   c(n-1, k-1) of those exist
        subsets EXCLUDING 1   c(n-1, k) of these exist

        c(n,k) = c(n-1,k-1) + c(n-1, k)

        c(4,2) = c(3,1) + c(3,2)
               =   3    + c(3,1) = 6

        ABCD

        AB
        AC
        AD
        BC
        BD
        CD

        fact:
        The product of k consecutive integers
        is divisble by k!