Question 847178: How many different groups of three can be formed with six items?
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! 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 
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.
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