simple method to count binomial coefficients https://en.wikipedia.org/wiki/Binomial_coefficient

binomial.rb

module Probability

  def binomial(n, k)
    return 1 if k == 0 || n == k
    if n < 0 || k < 0
      raise ArgumentError, 'both arguments must be greater than 0'
    elsif k >= n
      raise ArgumentError, 'second argument can\'t be greater than first one'
    end

    ( 1+n-k..n ).inject(:*) / (1..k).inject(:*)
  end

end

binomial_spec.rb

require_relative 'binomial'

describe Probability do
  let(:dummy_class) do
    Class.new { extend Probability}
  end
  let(:subject) {dummy_class}

  it 'binominal gives correct answers' do
    expect(subject.binomial(8,4)).to eql 70
    expect(subject.binomial(5,2)).to eql 10
    expect(subject.binomial(5,3)).to eql 10
  end

  it 'binominal returns 1 if both exponents are the same' do
    expect(subject.binomial(3,3)).to eql 1
  end

  it 'binominal returns 1 if both the second exponent is equal to 0' do
    expect(subject.binomial(7,0)).to eql 1
  end

  context 'binominal raises errors' do

    it 'for wrong order of arguments' do
      expect { subject.binomial(1,2) }.to raise_error(ArgumentError)
    end

    it 'for negative numbers in arguments ' do
      expect { subject.binomial(-1,-2) }.to raise_error(ArgumentError)
    end

  end
end