6. Binomial coefficients

The binomial coefficient of N and K gives the number of ways that you can pick N values from a set of K values. The binomial coefficient is usually written as and is pronounced N choose K.

For example, suppose you have a set of four values, {A, B, C, D}. The possible ways to select two of those values are {A, B}, {A, C}, {A, D}, {B, C}, {B, D}, and {C, D}. There are six possible ways to select two items from the original set of four items, so =6.

You can use the following formula to calculate binomial coefficients:

For the example where we select two items out of four, the formula gives the following:

Write a program that calculates binomial coefficients. Test your program by verifying the following values: