Exercise 2: Forming a 3-Person Team From 8 People — Possible Solution
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IDENTIFYING WHICH FORMULA APPLIES
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This is a combination problem - unlike Exercise 1's medal ranking,
team membership has no internal ordering. Being selected as one of
the three team members is the same outcome regardless of which "slot"
you're imagined to fill - there's no 1st/2nd/3rd distinction among
teammates.

SETTING UP AND COMPUTING THE CALCULATION
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This is C(n, r) with n = 8 and r = 3:

  C(8, 3) = 8! / (3! x 5!)
          = (8 x 7 x 6) / (3 x 2 x 1)
          = 336 / 6
          = 56

So there are 56 different possible 3-person teams from a pool of 8
people.

WHY THIS ANSWER IS SMALLER THAN EXERCISE 1's OWN 336
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Per this chapter, "C(n,r) = P(n,r) / r! - every combination of r
items corresponds to exactly r! different permutations." Here, r = 3,
so r! = 3! = 6. Exercise 1's own permutation count (336) counted every
possible ORDERED arrangement of 3 racers among medal positions - which
means each specific group of 3 people was counted 6 separate times
(once for every one of the 3! = 6 ways to assign gold/silver/bronze
among that same trio).

Combinations remove exactly that redundancy: dividing 336 by 6 gives
56, because each of the 56 distinct 3-person groups was being counted
6 times over in the permutation total, once for every possible
ordering of that same group.

WHY THIS CONFIRMS THE CHAPTER'S OWN RELATIONSHIP DIRECTLY
------------------------------
336 / 6 = 56 is not a coincidence - it's a direct numerical
verification of C(n,r) = P(n,r)/r! using this exercise's own two
results. The same 8 people and the same "choose 3" question produce a
6x larger count the moment order is allowed to matter, exactly
matching the general relationship this chapter establishes between the
two formulas.

WHY THIS WORKS AS AN ANSWER
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It justifies why this specific question is a combination rather than a
permutation, computes C(8,3) directly, and explains the size
difference from Exercise 1 by connecting it explicitly to the
r!-division relationship this chapter established between combinations
and permutations, verified with the exercise's own actual numbers.