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Counting pairs of animals


Unordered outcomes (counting)counting on $4$ pairs of glovesMaximum unique pairings between two lists of repeated itemsNumber of Possible Pairs from Two Setshow many permutation without fixed points from 2n to NxNFeller's Probability - Counting problem of pairs of shoes.Help distinguishing between factorials, $^nC_r$ and $^nP_r$Combinatorics card counting question.Number of possible permutations of three pairs of socks, one blue, one black, and one white?Counting with Permutations













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Old MacDonald has $5$ chickens, $4$ donkeys, and $7$ emus. How many ways can he pair up the animals so that every pair consists of animals of different species? (The order of the animals within each pair does not matter, and the order among the pairs does not matter. Assume that all animals are distinguishable.)




The answer I have currently is $83$ since there are $5*4=20$ possible pairs for (Chicken, Donkey), $5*7=35$ possible pairs for (Chicken, Emu), $4*7=28$ possible pairs for (Donkey, Emu). Then I added them up: $20+35+28=83$. Is this correct?










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$endgroup$
















    1












    $begingroup$



    Old MacDonald has $5$ chickens, $4$ donkeys, and $7$ emus. How many ways can he pair up the animals so that every pair consists of animals of different species? (The order of the animals within each pair does not matter, and the order among the pairs does not matter. Assume that all animals are distinguishable.)




    The answer I have currently is $83$ since there are $5*4=20$ possible pairs for (Chicken, Donkey), $5*7=35$ possible pairs for (Chicken, Emu), $4*7=28$ possible pairs for (Donkey, Emu). Then I added them up: $20+35+28=83$. Is this correct?










    share|cite|improve this question











    $endgroup$














      1












      1








      1





      $begingroup$



      Old MacDonald has $5$ chickens, $4$ donkeys, and $7$ emus. How many ways can he pair up the animals so that every pair consists of animals of different species? (The order of the animals within each pair does not matter, and the order among the pairs does not matter. Assume that all animals are distinguishable.)




      The answer I have currently is $83$ since there are $5*4=20$ possible pairs for (Chicken, Donkey), $5*7=35$ possible pairs for (Chicken, Emu), $4*7=28$ possible pairs for (Donkey, Emu). Then I added them up: $20+35+28=83$. Is this correct?










      share|cite|improve this question











      $endgroup$





      Old MacDonald has $5$ chickens, $4$ donkeys, and $7$ emus. How many ways can he pair up the animals so that every pair consists of animals of different species? (The order of the animals within each pair does not matter, and the order among the pairs does not matter. Assume that all animals are distinguishable.)




      The answer I have currently is $83$ since there are $5*4=20$ possible pairs for (Chicken, Donkey), $5*7=35$ possible pairs for (Chicken, Emu), $4*7=28$ possible pairs for (Donkey, Emu). Then I added them up: $20+35+28=83$. Is this correct?







      combinatorics






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      edited Mar 22 at 2:10









      Eevee Trainer

      10k31740




      10k31740










      asked Mar 22 at 1:59









      sumisumi

      654




      654




















          2 Answers
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          active

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          1












          $begingroup$

          Correct - you get the same thing by counting all possible pairs and subtracting the ones with two of the same type ..



          enter image description here






          share|cite|improve this answer









          $endgroup$




















            0












            $begingroup$

            Yup, your solution is correct.




            Making this a community wiki post since it's not like I have anything to add. If anyone else does, they're welcome to, though!






            share|cite|improve this answer











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              2






              active

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              active

              oldest

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              1












              $begingroup$

              Correct - you get the same thing by counting all possible pairs and subtracting the ones with two of the same type ..



              enter image description here






              share|cite|improve this answer









              $endgroup$

















                1












                $begingroup$

                Correct - you get the same thing by counting all possible pairs and subtracting the ones with two of the same type ..



                enter image description here






                share|cite|improve this answer









                $endgroup$















                  1












                  1








                  1





                  $begingroup$

                  Correct - you get the same thing by counting all possible pairs and subtracting the ones with two of the same type ..



                  enter image description here






                  share|cite|improve this answer









                  $endgroup$



                  Correct - you get the same thing by counting all possible pairs and subtracting the ones with two of the same type ..



                  enter image description here







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Mar 22 at 2:17









                  WW1WW1

                  7,3501712




                  7,3501712





















                      0












                      $begingroup$

                      Yup, your solution is correct.




                      Making this a community wiki post since it's not like I have anything to add. If anyone else does, they're welcome to, though!






                      share|cite|improve this answer











                      $endgroup$

















                        0












                        $begingroup$

                        Yup, your solution is correct.




                        Making this a community wiki post since it's not like I have anything to add. If anyone else does, they're welcome to, though!






                        share|cite|improve this answer











                        $endgroup$















                          0












                          0








                          0





                          $begingroup$

                          Yup, your solution is correct.




                          Making this a community wiki post since it's not like I have anything to add. If anyone else does, they're welcome to, though!






                          share|cite|improve this answer











                          $endgroup$



                          Yup, your solution is correct.




                          Making this a community wiki post since it's not like I have anything to add. If anyone else does, they're welcome to, though!







                          share|cite|improve this answer














                          share|cite|improve this answer



                          share|cite|improve this answer








                          answered Mar 22 at 2:08


























                          community wiki





                          Eevee Trainer




























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