Question 1141004: I have two hats. In one hat are balls numbered 1 through 15. In the other hat are balls numbered 16 through 25. I first choose a hat, then from that hat, I choose 3 balls, without replacing the balls between selections. How many different ordered selections of 3 balls are possible?
I made my solution and tell me if it's correct or not. But if any mistakes are to be found, I'd like to ask for clarifications. So, here's my solution:
2(15P3 + 9P3)
since there are two hats there's going to be 2 ways. And for that, since there are two cases to choose either we could have the first hat from 1 through 15 or
16 through 25 where either we get 3 from the 1st or 2nd - we then add it. Since without replacement, we could say that the number is to be reduce from succeeding stages(say 15,14,13 or in a manner of 15P3, in the first hat and same thing with the second hat).
For the answer, I get 6468 ordered selections.
Answer by ikleyn(52879)   (Show Source):
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