hi! I've been stuck on this problem for a while now, so any help would really be appreciated!
sorry if I put this in the wrong category, i didn't know where it should go.
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.)
here are some thoughts;
Initially, I tried just having 5*4 (chicken-donkey) + 4*7 (donkey-emu) + 7*5 (emu-chicken) = 83. But I think the reason why that doesn't work is because the animals must be all paired at the same time.
I realized that there must be one emu-chicken pairing, so that the amount of chickens and donkeys remaining would be equal. So there would be 6 emus, 4 donkeys, and 4 chickens remaining to pair. Then I don't know what to do next, except that we must find out the amount of emu-chicken pairs, and the amount of emu-donkey pairs. Then, if there is any extra animals, I think we could pair them with each other. I'm not sure, though. Maybe there are also other possibilities, which is what I'm stuck on.
sorry if I put this in the wrong category, i didn't know where it should go.
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.)
here are some thoughts;
Initially, I tried just having 5*4 (chicken-donkey) + 4*7 (donkey-emu) + 7*5 (emu-chicken) = 83. But I think the reason why that doesn't work is because the animals must be all paired at the same time.
I realized that there must be one emu-chicken pairing, so that the amount of chickens and donkeys remaining would be equal. So there would be 6 emus, 4 donkeys, and 4 chickens remaining to pair. Then I don't know what to do next, except that we must find out the amount of emu-chicken pairs, and the amount of emu-donkey pairs. Then, if there is any extra animals, I think we could pair them with each other. I'm not sure, though. Maybe there are also other possibilities, which is what I'm stuck on.
