title: How many students can you put into a hash table before a collision occurs?
body: <p>My professor gave us this slide while explaining Hash Collision probabilities:</p>
  
  <p><a href="https://i.stack.imgur.com/xUBaE.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/xUBaE.jpg" alt="enter image description here"></a></p>
  
  <p>When I looked up the probabilities of two people having the same birthday in the "Birthday Paradox", I found on <a href="https://en.wikipedia.org/wiki/Birthday_problem#Calculating_the_probability" rel="nofollow noreferrer">Wikipedia and other sources</a> that the probability at n=10 is supposed to be 11.7. In fact every value I found and calculated myself using his formula was different from the professor's slide.</p>
  
  <p>So my question is: when he asks "How many students can we hash into our table before a collision occurs," is that different from calculating the probability that any 2 students has the same birthday? </p>
  
  <p>And if so, is there a formula for that? </p>
  
  <p>Or was his slide was just wrong?</p>