SOLUTION: How many different sets of 2 jurors can be selected from the group of seven? List the sample space using A, B, C, and D for the men and J, K, L for the women.

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Question 898938: How many different sets of 2 jurors can be selected from the group of seven?
List the sample space using A, B, C, and D for the men and J, K, L for the women.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are 12 choices for slot 1 and 11 (12-1) choices for slot 2

12*11 = 132

You'd have 132 different ways to pick 2 people if order mattered. Order doesn't matter which means you're overcounting. For instance, AB is the same as BA. So every group is counted twice. To fix this, you divide by 2.


132/2 = 66


There are 66 different groups of 2 people.

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Sample Space: 

AB, AC, AD, AE, AF, AG, AH, AI, AJ, AK, AL
    BC, BD, BE, BF, BG, BH, BI, BJ, BK, BL
        CD, CE, CF, CG, CH, CI, CJ, CK, CL
            DE, DF, DG, DH, DI, DJ, DK, DL
                EF, EG, EH, EI, EJ, EK, EL
                    FG, FH, FI, FJ, FK, FL
                        GH, GI, GJ, GK, GL
                            HI, HJ, HK, HL
                                IJ, IK, IL
                                    JK, JL
                                        KL

Each row is written so that the first letter of each pair is the same (eg: top row is row A, second row is row B, etc). There are 11 pairs in row A, 10 in row B, 9 in row C ..., all the way down to 1 in row K.

So there are 11+10+9+8+7+6+5+4+3+2+1 = 66 different pairs where order doesn't matter.