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How do I list all possible pairs?

The United Nations The World Court World Organization of the World Scout Movement Amnesty International The International Committee of the Red Cross CARE I came up with the answer 21 by listing them in a piece of paper. Is there a trick to how you can get the answer faster? I'm also suppose to list the odds of The UNited Nations and the Amnesty International being together? Actually, it's a total of 7 organizations I forgot to add one. That's how I came up with 21.

Public Comments

1. There are 6 distinct organizations...there would be [6 C 2] pairs [6 * 5]/2 = 15 if you came up with 21, you are listing some pairs multiple times ! @Σ
2. You have six organizations taken 2 at a time. The number of possible pairs is 6C2 = 6!/(4! 2!) = 6 • 5/2 = 15 The second part is 1/15
3. I take it you want to list all possible pairs of organizations from the 6 you have given. For ease of typing i shall use the letters....... a b c d e f ..... to stand for the organizations. Beginning with 'a' i go through the other 5 to make the pair so ..... ab ac ad ae af Next i begin with the next letter along , 'b' and go through the remaining 4 to make the pair so ..... bc bd be bf thus there will be 5 + 4 + 3 +2 +1 (the last pair in my enumeration would be 'ef') a total of 15 pairs only! since each pairing is equally likely, each particular pair like 'ad' will have odds of 15:1