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If Japan has a total of 132 cat species and you happen to catch 3 species...

If Japan has a total of 132 cat species and you happen to catch 3 species in an observational experiment using cat treats, what is the total number of possible combinations of species that you captured? I would also like to see how the problem is done so I can learn from it. Thank you!

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Answer #1

You can pick one species out of 132 in 132 number of ways. There are still 132 species in Japan (unless one species had just one individual left, or unless you do not mind getting one species repeated). In the second instant, you can still pick up one species in 132 number of ways, and so you can in the third instant. Thus, you have 132 x 132 x 132 = 2299968 number of possibilities

In cases you do not want to repeat a species (that is, you do not want more that one sample from the same species), after the first instance, you will have 132 - 1 = 131 ways to select the second sample, and 130 ways to select the thirst sample. In that case, the total number of possibilities will be 132 x 131 x 130 = 2247960.

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