Combinations vs Permutation

Combinations vs Permutation

1. Does order matter

   • yes
     • permutation
       • are some items identical
         • yes
           • n!/(p!q!r!s!)
             • # of ways to rearrange the letters in KAYAK 5!/(2!2!)
         • no
           • are we selecting all of the items
             • yes
               • n!
                 • ways to arrange 6 books on a shelf 6!
             • no
               • nPr = n!/(n-r)!
                 • ways to choose a captain and assistant from 8 players 8P2
   • no
     • combination
       • do we know the exact number of items selected
         • yes
           • are some items identical
             • yes
               • consider cases
             • no
               • nCr=n!/(n-r)!r!
         • no
           • are some items identical
             • yes
               • (p+1)(q+1)(r+1)...
             • no
               • 2^n -1