Small Julia utilities for counting

counting.jl

# C(n,r)
function C(n::Int, r::Int)
  return (factorial(n)) / (factorial(r)*factorial(n - r))
end
# P(n,r)
function P(n::Int, r::Int)
  return (factorial(n) / factorial(n -r))
end
# Sum of a function in a j .. n range
function ∑(j::Int, n::Int, f::Function)
  ans = 0
  for i = j : n
    ans += f(n, i)
  end
end