Basic combinatorics in C# is a straight forward task for relatively small numbers like (100!). This is a helper class I wrote when I was asked to write an online lottery system.

Keep in mind though, that for bigger numbers (above 100!) you will need Arbitrary-precision arithmetic.

Here is the code and please, if someone knows a faster way or has some suggestions let me now!

public class BasicCombinatorics
{

    /// 

    /// One object in each position,
    /// With elementary counting,
    /// With repetitions,
    /// With grouping of same objects
    /// 
    /// Number of objects
    /// Groups of same objects
    /// Number of permutations with groups of same objects
    public double PermutationsSimilarGroups(int n, List ni)
    {
        var p = 1.0d;
        foreach (var i in ni)
            p *= Factorial(i);

        return p / Factorial(n);
    }

    /// 

    /// One object in each position,
    /// With elementary counting,
    /// With repetitions,
    /// No groups of same objects
    /// 
    /// Number of objects
    /// Number of positions
    /// Number of provisions with repetition of n per k
    public double ProvisionsReps(int n, int k)
    {
        return Math.Pow(n, k);
    }

    /// 

    /// One object in each position,
    /// With elementary counting,
    /// No repetitions
    /// 
    /// Number of objects
    /// Number of positions
    /// Number of simple provisions
    public double SimpleProvisions(int n, int k)
    {
        return Factorial(n) / Factorial(n - k);
    }

    /// 

    /// One object in each position,
    /// No elementary counting,
    /// With repetitions
    /// 
    /// Number of objects
    /// Number of positions
    /// Number of combinations
    public double CombinationsΡeps(int n, int k)
    {
        return Factorial(n + k - 1) / (Factorial(k) * Factorial(n - 1));
    }

    /// 

    /// One object in each position,
    /// No elementary counting,
    /// No repetitions
    /// 
    /// Number of objects
    /// Number of positions
    /// Number of simple combinations
    public double SimpleCombinations(int n, int k)
    {
        return Factorial(n) / (Factorial(k) * Factorial(n - k));
    }

    /// 

    /// Many object in each position,
    /// With same objects
    /// 
    /// Number of objects
    /// Number of positions
    /// Number of combinations of same objects
    public double SameObjectsInSlots(int n, int m)
    {
        return Factorial(m + n - 1) / (Factorial(n) * Factorial(m - 1));
    }

    /// 

    /// Many object in each position,
    /// No same objects,
    /// With distinguished objects
    /// 
    /// Number of objects
    /// Number of positions
    /// Number of combinations of distinguished objects
    public double DifObjectsInSlotsBySeries(int n, int m)
    {
        return Factorial(m + n - 1) / Factorial(m - 1);
    }

    /// 

    /// Many object in each position,
    /// No same objects,
    /// No distinguished objects
    /// 
    /// Number of objects
    /// Number of positions
    /// Number of combinations
    public double DifObjectsInSlots(int n, int m)
    {
        return Math.Pow(m, n);
    }

    /// 

    /// Factorial of a number
    /// 
    /// A number for factorial (n!)
    /// n!
    public double Factorial(int n)
    {
        double result = 1;
        for (int i = n; i >= 1; i--)
            result *= i;
        return result;
    }

    /// 

    /// Sum of a number (Σn)
    /// 
    /// A number for sum (Σn)
    /// Σn
    public double Sum(int n)
    {
        double result = 0;
        for (int i = n; i >= 1; i--)
            result += i;
        return result;
    }
}