Question 847178
Since you are looking at groups, order does not matter. In other words: a group with Billy, Bob, and Mike is no different than  Billy, Mike, and Bob.

With this in mind what we want is a combination.  So we use (6 choose 3) = 20. You can calculate this using the nCr [just type 6 nCR 3] ability of your calculator or you can use the formula    {{{ 6! /(3!(6-3)!)}}} 

You can see that there are 20 if we name these item 1,2,3,4,5,6

Possible groups
123  - #1
124  - #2
125  - #3
126  - #4
134  - #5
135  - #6
136  - #7
145  - #8
146  - #9
156  - #10
234  - #11
235  - #12
236  - #13
245  - #14
246  - #15
256  - #16
345  - #17
346  - #18
356  - #19
456  - #20

Checks out.