# How to make a list of the possible pairs of 4 objects from a set of 6?

Posted 9 years ago
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 Example: set of 6 objects =( a, b, c, d, e, f) 2 possible pair coming from 4 objects from the set: ab, ec . No repetitions allowed. ab and ba have to be considered as different pairsThanks in advance! regards lorenzo
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Posted 9 years ago
 Hi Lorenzo,my idea goes like this: calculate all permutations; make 3 pairs of every permutation; take only the first two pairs into account (using Most); delete the duplicates; two elements are considered as duplicates, when foo[x1,x2]+foo[y1,y2] gives identical expressions. "foo" is basically NOT orderless, otherwise left undefined. As typical for Mathematica the code is very much shorter than any explanation: ClearAll["Global*"] objects = {a, b, c, d, e, f}; DeleteDuplicatesBy[ Most /@ (Partition[#, 2] & /@ Permutations[objects]), foo @@ #[[1]] + foo @@ #[[2]] &] Hope I am correct ... Henrik
Posted 9 years ago
 Thankyou Henrik. But I expected only 360 pairs. Your computation gives me too many pairs. bye lorenzo
Posted 9 years ago
 Hi Lorenzo,my code gives exactly 180 pairs (of pairs)! That is because e.g. {{a,b},{c,d}} and {{c,d},{a,b}} are considered identical - in contrast to Davids solution. It depends on what you want.Cheers Henrik
Posted 9 years ago
 How about this: set = {a, b, c, d, e, f} step1 = Subsets[set, {4}] step2 = Flatten[Permutations /@ step1, 1]; Partition[#, 2] & /@ step2 giving: {{{a, b}, {c, d}}, {{a, b}, {d, c}}, {{a, c}, {b, d}}, {{a, c}, {d, b}}, {{a, d}, {b, c}}, {{a, d}, {c, b}}, {{b, a}, {c, d}}, {{b, a}, {d, c}}, {{b, c}, {a, d}}, {{b, c}, {d, a}}, {{b, d}, {a, c}}, {{b, d}, {c, a}}, {{c, a}, {b, d}}, {{c, a}, {d, b}}, {{c, b}, {a, d}}, {{c, b}, {d, a}}, {{c, d}, {a, b}}, {{c, d}, {b, a}}, {{d, a}, {b, c}}, {{d, a}, {c, b}}, {{d, b}, {a, c}}, {{d, b}, {c, a}}, {{d, c}, {a, b}}, {{d, c}, {b, a}}, {{a, b}, {c, e}}, {{a, b}, {e, c}}, {{a, c}, {b, e}}, {{a, c}, {e, b}}, {{a, e}, {b, c}}, {{a, e}, {c, b}}, {{b, a}, {c, e}}, {{b, a}, {e, c}}, {{b, c}, {a, e}}, {{b, c}, {e, a}}, {{b, e}, {a, c}}, {{b, e}, {c, a}}, {{c, a}, {b, e}}, {{c, a}, {e, b}}, {{c, b}, {a, e}}, {{c, b}, {e, a}}, {{c, e}, {a, b}}, {{c, e}, {b, a}}, {{e, a}, {b, c}}, {{e, a}, {c, b}}, {{e, b}, {a, c}}, {{e, b}, {c, a}}, {{e, c}, {a, b}}, {{e, c}, {b, a}}, {{a, b}, {c, f}}, {{a, b}, {f, c}}, {{a, c}, {b, f}}, {{a, c}, {f, b}}, {{a, f}, {b, c}}, {{a, f}, {c, b}}, {{b, a}, {c, f}}, {{b, a}, {f, c}}, {{b, c}, {a, f}}, {{b, c}, {f, a}}, {{b, f}, {a, c}}, {{b, f}, {c, a}}, {{c, a}, {b, f}}, {{c, a}, {f, b}}, {{c, b}, {a, f}}, {{c, b}, {f, a}}, {{c, f}, {a, b}}, {{c, f}, {b, a}}, {{f, a}, {b, c}}, {{f, a}, {c, b}}, {{f, b}, {a, c}}, {{f, b}, {c, a}}, {{f, c}, {a, b}}, {{f, c}, {b, a}}, {{a, b}, {d, e}}, {{a, b}, {e, d}}, {{a, d}, {b, e}}, {{a, d}, {e, b}}, {{a, e}, {b, d}}, {{a, e}, {d, b}}, {{b, a}, {d, e}}, {{b, a}, {e, d}}, {{b, d}, {a, e}}, {{b, d}, {e, a}}, {{b, e}, {a, d}}, {{b, e}, {d, a}}, {{d, a}, {b, e}}, {{d, a}, {e, b}}, {{d, b}, {a, e}}, {{d, b}, {e, a}}, {{d, e}, {a, b}}, {{d, e}, {b, a}}, {{e, a}, {b, d}}, {{e, a}, {d, b}}, {{e, b}, {a, d}}, {{e, b}, {d, a}}, {{e, d}, {a, b}}, {{e, d}, {b, a}}, {{a, b}, {d, f}}, {{a, b}, {f, d}}, {{a, d}, {b, f}}, {{a, d}, {f, b}}, {{a, f}, {b, d}}, {{a, f}, {d, b}}, {{b, a}, {d, f}}, {{b, a}, {f, d}}, {{b, d}, {a, f}}, {{b, d}, {f, a}}, {{b, f}, {a, d}}, {{b, f}, {d, a}}, {{d, a}, {b, f}}, {{d, a}, {f, b}}, {{d, b}, {a, f}}, {{d, b}, {f, a}}, {{d, f}, {a, b}}, {{d, f}, {b, a}}, {{f, a}, {b, d}}, {{f, a}, {d, b}}, {{f, b}, {a, d}}, {{f, b}, {d, a}}, {{f, d}, {a, b}}, {{f, d}, {b, a}}, {{a, b}, {e, f}}, {{a, b}, {f, e}}, {{a, e}, {b, f}}, {{a, e}, {f, b}}, {{a, f}, {b, e}}, {{a, f}, {e, b}}, {{b, a}, {e, f}}, {{b, a}, {f, e}}, {{b, e}, {a, f}}, {{b, e}, {f, a}}, {{b, f}, {a, e}}, {{b, f}, {e, a}}, {{e, a}, {b, f}}, {{e, a}, {f, b}}, {{e, b}, {a, f}}, {{e, b}, {f, a}}, {{e, f}, {a, b}}, {{e, f}, {b, a}}, {{f, a}, {b, e}}, {{f, a}, {e, b}}, {{f, b}, {a, e}}, {{f, b}, {e, a}}, {{f, e}, {a, b}}, {{f, e}, {b, a}}, {{a, c}, {d, e}}, {{a, c}, {e, d}}, {{a, d}, {c, e}}, {{a, d}, {e, c}}, {{a, e}, {c, d}}, {{a, e}, {d, c}}, {{c, a}, {d, e}}, {{c, a}, {e, d}}, {{c, d}, {a, e}}, {{c, d}, {e, a}}, {{c, e}, {a, d}}, {{c, e}, {d, a}}, {{d, a}, {c, e}}, {{d, a}, {e, c}}, {{d, c}, {a, e}}, {{d, c}, {e, a}}, {{d, e}, {a, c}}, {{d, e}, {c, a}}, {{e, a}, {c, d}}, {{e, a}, {d, c}}, {{e, c}, {a, d}}, {{e, c}, {d, a}}, {{e, d}, {a, c}}, {{e, d}, {c, a}}, {{a, c}, {d, f}}, {{a, c}, {f, d}}, {{a, d}, {c, f}}, {{a, d}, {f, c}}, {{a, f}, {c, d}}, {{a, f}, {d, c}}, {{c, a}, {d, f}}, {{c, a}, {f, d}}, {{c, d}, {a, f}}, {{c, d}, {f, a}}, {{c, f}, {a, d}}, {{c, f}, {d, a}}, {{d, a}, {c, f}}, {{d, a}, {f, c}}, {{d, c}, {a, f}}, {{d, c}, {f, a}}, {{d, f}, {a, c}}, {{d, f}, {c, a}}, {{f, a}, {c, d}}, {{f, a}, {d, c}}, {{f, c}, {a, d}}, {{f, c}, {d, a}}, {{f, d}, {a, c}}, {{f, d}, {c, a}}, {{a, c}, {e, f}}, {{a, c}, {f, e}}, {{a, e}, {c, f}}, {{a, e}, {f, c}}, {{a, f}, {c, e}}, {{a, f}, {e, c}}, {{c, a}, {e, f}}, {{c, a}, {f, e}}, {{c, e}, {a, f}}, {{c, e}, {f, a}}, {{c, f}, {a, e}}, {{c, f}, {e, a}}, {{e, a}, {c, f}}, {{e, a}, {f, c}}, {{e, c}, {a, f}}, {{e, c}, {f, a}}, {{e, f}, {a, c}}, {{e, f}, {c, a}}, {{f, a}, {c, e}}, {{f, a}, {e, c}}, {{f, c}, {a, e}}, {{f, c}, {e, a}}, {{f, e}, {a, c}}, {{f, e}, {c, a}}, {{a, d}, {e, f}}, {{a, d}, {f, e}}, {{a, e}, {d, f}}, {{a, e}, {f, d}}, {{a, f}, {d, e}}, {{a, f}, {e, d}}, {{d, a}, {e, f}}, {{d, a}, {f, e}}, {{d, e}, {a, f}}, {{d, e}, {f, a}}, {{d, f}, {a, e}}, {{d, f}, {e, a}}, {{e, a}, {d, f}}, {{e, a}, {f, d}}, {{e, d}, {a, f}}, {{e, d}, {f, a}}, {{e, f}, {a, d}}, {{e, f}, {d, a}}, {{f, a}, {d, e}}, {{f, a}, {e, d}}, {{f, d}, {a, e}}, {{f, d}, {e, a}}, {{f, e}, {a, d}}, {{f, e}, {d, a}}, {{b, c}, {d, e}}, {{b, c}, {e, d}}, {{b, d}, {c, e}}, {{b, d}, {e, c}}, {{b, e}, {c, d}}, {{b, e}, {d, c}}, {{c, b}, {d, e}}, {{c, b}, {e, d}}, {{c, d}, {b, e}}, {{c, d}, {e, b}}, {{c, e}, {b, d}}, {{c, e}, {d, b}}, {{d, b}, {c, e}}, {{d, b}, {e, c}}, {{d, c}, {b, e}}, {{d, c}, {e, b}}, {{d, e}, {b, c}}, {{d, e}, {c, b}}, {{e, b}, {c, d}}, {{e, b}, {d, c}}, {{e, c}, {b, d}}, {{e, c}, {d, b}}, {{e, d}, {b, c}}, {{e, d}, {c, b}}, {{b, c}, {d, f}}, {{b, c}, {f, d}}, {{b, d}, {c, f}}, {{b, d}, {f, c}}, {{b, f}, {c, d}}, {{b, f}, {d, c}}, {{c, b}, {d, f}}, {{c, b}, {f, d}}, {{c, d}, {b, f}}, {{c, d}, {f, b}}, {{c, f}, {b, d}}, {{c, f}, {d, b}}, {{d, b}, {c, f}}, {{d, b}, {f, c}}, {{d, c}, {b, f}}, {{d, c}, {f, b}}, {{d, f}, {b, c}}, {{d, f}, {c, b}}, {{f, b}, {c, d}}, {{f, b}, {d, c}}, {{f, c}, {b, d}}, {{f, c}, {d, b}}, {{f, d}, {b, c}}, {{f, d}, {c, b}}, {{b, c}, {e, f}}, {{b, c}, {f, e}}, {{b, e}, {c, f}}, {{b, e}, {f, c}}, {{b, f}, {c, e}}, {{b, f}, {e, c}}, {{c, b}, {e, f}}, {{c, b}, {f, e}}, {{c, e}, {b, f}}, {{c, e}, {f, b}}, {{c, f}, {b, e}}, {{c, f}, {e, b}}, {{e, b}, {c, f}}, {{e, b}, {f, c}}, {{e, c}, {b, f}}, {{e, c}, {f, b}}, {{e, f}, {b, c}}, {{e, f}, {c, b}}, {{f, b}, {c, e}}, {{f, b}, {e, c}}, {{f, c}, {b, e}}, {{f, c}, {e, b}}, {{f, e}, {b, c}}, {{f, e}, {c, b}}, {{b, d}, {e, f}}, {{b, d}, {f, e}}, {{b, e}, {d, f}}, {{b, e}, {f, d}}, {{b, f}, {d, e}}, {{b, f}, {e, d}}, {{d, b}, {e, f}}, {{d, b}, {f, e}}, {{d, e}, {b, f}}, {{d, e}, {f, b}}, {{d, f}, {b, e}}, {{d, f}, {e, b}}, {{e, b}, {d, f}}, {{e, b}, {f, d}}, {{e, d}, {b, f}}, {{e, d}, {f, b}}, {{e, f}, {b, d}}, {{e, f}, {d, b}}, {{f, b}, {d, e}}, {{f, b}, {e, d}}, {{f, d}, {b, e}}, {{f, d}, {e, b}}, {{f, e}, {b, d}}, {{f, e}, {d, b}}, {{c, d}, {e, f}}, {{c, d}, {f, e}}, {{c, e}, {d, f}}, {{c, e}, {f, d}}, {{c, f}, {d, e}}, {{c, f}, {e, d}}, {{d, c}, {e, f}}, {{d, c}, {f, e}}, {{d, e}, {c, f}}, {{d, e}, {f, c}}, {{d, f}, {c, e}}, {{d, f}, {e, c}}, {{e, c}, {d, f}}, {{e, c}, {f, d}}, {{e, d}, {c, f}}, {{e, d}, {f, c}}, {{e, f}, {c, d}}, {{e, f}, {d, c}}, {{f, c}, {d, e}}, {{f, c}, {e, d}}, {{f, d}, {c, e}}, {{f, d}, {e, c}}, {{f, e}, {c, d}}, {{f, e}, {d, c}}} `
Posted 9 years ago
 Thanks a lot! regards lorenzo