A programming language has 10 different instructions. How many five-instruction programs can be written in this language if no instruction is repeated? How many seven-instruction programs?

n_instruction_programs.rb

#!/usr/bin/ruby

def factorial n
    f = n
    for i in (n - 1).downto(1)
        f *= i
        i -= 1
    end
    return f
end
def combinations_with_repetition n, r
    return factorial(n + r - 1) / (factorial(r) * factorial(n - 1))
end
def combinations_without_repetition n, r
    return factorial(n) / (factorial(r) * factorial(n - r))
end
def permutations_with_repetition n, r
    return n ** r
end
def permutations_without_repetition n, r
    return factorial(n) / factorial(n - r)
end

puts "#{combinations_with_repetition 10, 5} 5 instruction programs (combinations_with_repetition)"
puts "#{combinations_without_repetition 10, 5} 5 instruction programs (combinations_without_repetition)"
puts "#{permutations_with_repetition 10, 5} 5 instruction programs (permutations_with_repetition)"
puts "#{permutations_without_repetition 10, 5} 5 instruction programs (permutations_without_repetition)"

puts "#{combinations_with_repetition 10, 7} 7 instruction programs (combinations_with_repetition)"
puts "#{combinations_without_repetition 10, 7} 7 instruction programs (combinations_without_repetition)"
puts "#{permutations_with_repetition 10, 7} 7 instruction programs (permutations_with_repetition)"
puts "#{permutations_without_repetition 10, 7} 7 instruction programs (permutations_without_repetition)"