title: Calculate probability that M out of N events will appear
body: <p>I have probabilities of 110 independent events. 
  I want to calculate for every number of events, that exactly that number of distinct events will appear.</p>
  
  <p>Example, if we have only three events</p>
  
  <pre><code>A = 0.45
  B = 0.65
  C = 0.73
  
  # Probability of none event
  P[0] = (1-A)*(1-B)*(1-C)
  
  # Probability of exaclty one event
  P[1] = A*(1-B)*(1-C)+(1-A)*B*(1-C)+(1-A)*(1-B)*C
  
  # Probability of exactly two events
  P[2] = A*B*(1-C)+A*(1-B)*C+(1-A)*B*C
  
  # Probability of exactly three events
  P[3] = A*B*C
  </code></pre>
  
  <p>Is realistic to compute it for 110 events under 1 hour?</p>
  
  <p>If yes, how to do it in any programming language?</p>