greaterthan

The problem: A set of cards is numbered 1 through 5. Which of the two quantities is larger? Quantity A The number of ways to pick 3 of the 5 cards such that card number 1 is included Quantity B The number of ways to pick 3 of the 5 cards such that card number 1 is excluded Official Answer: The total number of ways to choose 3 out of 10 cards is (5!) / (3!)(2!) = 10 Since you have to choose a 1 for Quantity A, the number of ways to choose the remaining 2 out of 4 cards is: (4!) / (2!)(2!) = 6 = Quantity A So the number of combinations EXCLUDING the number 1 must be 10-6 = 4 = Quantity B HOWEVER, I encountered the attached problem and worked through it assuming ordered mattered, as in for Quantity A, if you picked a 1 first, then a 2, and then a 3, it was different from picking a 2 first, and then a 1, and finally a 3. So my calculation for Quantity A was 4*3 (four ways to choose the first card, and three ways to choose the second) = 12 ways to choose two cards, and then multiplied that by 3, because the number 1 could be picked first, second, or third in any of those combinations. For Quantity B, the calculation was merely 4*3*2 because excluding the 1 there are 4 options for the first card, 3 for the second, and 2 for the third. It appears as though the explanation assumes that every group with the same cards are the same no matter what order they were picked in. Is this just a poorly worded question that wouldn't be on the actual GRE? Or what am I missing that indicates that those groups are different? Thanks!