Combinations

Combinations are permutations where the order of things doesn't count. Here's an example:

We have a group of 5 kids:
DAVID BRYAN TONYA BJ CARRIE
We want to form 2-person groups to ride a ferris wheel. How many 2-person groups can we make? Well, here they are:
   <1>     <2>     <3>     <4>     <5>
  DAVID   DAVID   DAVID   DAVID   BRYAN
  BRYAN   TONYA     BJ    CARRIE  TONYA

   <6>     <7>     <8>     <9>     <10>
  BRYAN   BRYAN   TONYA   TONYA     BJ
    BJ    CARRIE    BJ    CARRIE  CARRIE
Why are there only 10 groups, when the number of permutations of 2 things out of a set of 5 would be:
5 x 4 = 20?
The reason is that half the permutations (10 of them) are missing! The missing 10 permutations are:
   <1>     <2>     <3>     <4>     <5>
  BRYAN   TONYA     BJ    CARRIE  TONYA
  DAVID   DAVID   DAVID   DAVID   BRYAN

   <6>     <7>     <8>     <9>     <10>
    BJ    CARRIE    BJ    CARRIE  CARRIE
  BRYAN   BRYAN   TONYA   TONYA     BJ
These are the same as the first 10, but the names are switched. These don't count, because a 2-person group of BRYAN and DAVID is the same as DAVID and BRYAN.

So, the number of COMBINATIONS (combinations is the name for order doesn't count) is: