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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.)

 Mar 13, 2021
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The number of ways of pairing the animals is C(5 + 4,2) + C(4 + 7,2) + C(7 + 5,2) = 157.

 Mar 14, 2021

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