In how many ways can (3) distinct red, blue and green flags be placed on a pole from top to bottom?

Correct answer: (6)

The direct answer is option B: 6 ways. The three flags are different, and all three are placed from top to bottom. For the top position there are 3 choices; after choosing one, 2 remain for the middle; the last flag goes at the bottom in 1 way. Thus the total is \(3\times2\times1=3!=6\). Option B is correct because each different top-to-bottom order is a different arrangement. Option A, 3, counts only the number of flags, not their possible orders. Option C, 9, does not follow the multiplication rule and would not correctly count arrangements. Option D, 12, is also an unsupported overcount. For example, red-blue-green and blue-red-green are different arrangements because their positions differ. Memory trick: three distinct objects in a line give \(3!=6\) orders.