title: Generate permutations
body: <p>I have n players to assign to n games. <code>10 &lt;= n &lt;= 20</code>. Each player can sign up for up to 3 games but will only get one. Different players have different score for each game they sign up for. </p>
  
  <p>Example with 10 players:</p>
  
  <p><a href="https://i.stack.imgur.com/Ggpbk.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Ggpbk.png" alt="score of 10 players"></a></p>
  
  <p>It's always possible to assign players x to game x but it will not always give the highest score in total.</p>
  
  <p>My goal is to get as high score as possible and I therefore want to test the different permutations. I could teoretically test all permutations and throw away the unfeasible ones but it will give me a hughe number of possibilities (<code>n!</code>). 
  Is it possible to reduce the problem with the sign up limit of max 3 games? Maybe this can be done more easily than my approach? Any thoughts?
  I'm working in Excel VBA.</p>
  
  <p>I hope you find this as interesting as I do ...</p>
  
  <p>Sorry if you find this unclear! My question is if it's possible to generate a subset of all the permutations. More precise only the feasible ones (which are the ones without any zero score).</p>