Combinations vs. Permutations

• Permutations ordered abc, acb, bac, bca, cab, cba

• Combinations unordered: abc

• Choose unordered subset k of n distinct objects

• Example: choose 2 from set of 3 (abc), ordered

• n! / ( n - k )! = 3! / ( 3 - 2 )! = 3! / 1! = 3 * 2 = 6

• ab, ac, ba, bc, ca, cb

• Example: choose 2 from 3, unordered

• ab (ab and ba), ac (ac and ca), bc (bc and cb)

• Number of combinations same as permutations divided by number of ways to permute subset