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Hi, Aldo, thank you for a GREAT response to this Milestone Activity. Each one is a conversation you have with your Tutorial Faculty for that competency. Let me respond to you by saying three things:
1) You never really responded to the prompt asking you to explain how the FCP is used within the Permutation Formula. You only discussed the formula. I was hoping you would say something to the effect that every factorial calculation CAN be thought of as an application of the FCP.
2) While you are correct about the Permutation Formula having the stipulation that order is involved, it turns out that both Permutations and Combinations have to involve dependent events, because of the underlying requirement for the experiment that you cannot replace what you select. That’s why the numbers keep going down each time you perform the experiment, and that’s why the factorial calculations lend themselves to the formula.
3) Okay, so we’ve established that you CAN use the Fundamental Counting Principle within the Permutation Formula, but the former requires independent events and the latter requires dependent events. That’s a problem we still have to resolve. Let’s use as example the fact that 5 P 3 = (5)(4)(3) = 60. If that’s an application of the Fundamental Counting Principle, then the events have to be independent. The ‘5’ is never a problem; the first selection is always independent of whatever came before it (which is nothing). How can we describe the ‘4’ and the ‘3’ in such a way that they are also independent events?