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.)
I thought the answer was 83, but it was wrong.
How many ways can you pair up 2 apples, 3 bananas, and 4 oranges? (With the same restrictions in your problem).
We first find how many pairs include an apple:
2 * 3 = 6
2 * 4 = 8
We then find how many pairs include a banana that is already not taken by the apple pairs
3 * 4 = 12
No more cases! (3 choose 2 is 3)
6 + 8 + 12 = 26
I'm not trying to be rude, but did you take the time to read through CU's solution? It was an example problem, not the actual problem itself. What CU intends to do here is teach you the steps of the problem, not just how to read the answer and enter it in some website. Please take the time to actually try to learn what he's teaching you here. Using his method, you would get the answer of 83, which you already said yourself is wrong.