# -*- coding: utf-8 -*-
import math
import random

def nCr(n,r):
    f = math.factorial
    out =  f(n) / (f(r)*f(n-r))
    return out

random.seed(10)

p_heads = 0.5
n_trials = 10
k_heads = 2

res = nCr(n_trials,k_heads)*(p_heads**k_heads)*((1.0-p_heads)**(n_trials-k_heads))
print res

step_max = 100000
success = 0.0 
for i in range(1,step_max):
  sum = 0 
  for j in range(1,n_trials+1):
    coin = random.random()
    if coin < p_heads:
        sum = sum + 1
  if sum == k_heads:
      success = success + 1.0      

print success,step_max,success/step_max