From (11) players (5) players are to be selected and exactly (2) of (3) special players are selected. How many ways are there?

Correct answer: (168)

The direct answer is option B, 168. Exactly two of the three special players must be selected. Choose those special players in C2 = 3 ways. There are 11 total players and 3 special players, so 8 non-special players remain. We need five players altogether, so after choosing two special players, choose three non-special players in C3 = 56 ways. By the multiplication principle, the total is C2 × C3 = 3×56 = 168. Option A, 112, is too small and results from an incorrect combination value. Option B, 168, is correct. Option C, 224, overcounts the choices. Option D, 336, counts even more than allowed and does not enforce exactly two special players. The word “exactly” is essential: one special player is not enough, while all three are not allowed. Memory cue: exactly two special = choose two from the special group and fill every remaining place from outside it.