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  3. The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3r

The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3r

游客2024-01-12  25
问题 The 5 letters in the list G, H, I, J, K are to be rearranged so that G is the 3rd letter in the list and H is not next to G. How many such rearrangements are there?
选项 A、60
B、36
C、24
D、12
E、6
答案 D
解析 When the 5 letters are rearranged, G is to be listed in the 3rd position and H cannot be next to G, so there are only two possible positions for H: 1st and 5th.
Case 1: In the rearranged list, G is in the 3rd position, H is in the 1st position, and each of the remaining 3 letters can be in any of the remaining 3 positions. The number of ways these remaining 3 letters can be arranged is 3!, or 6. Thus the total number of rearrangements in case 1 is 6.
Case 2: In the rearranged list, G is in the 3rd position, H is in the 5th position, and each of the remaining 3 letters can be in any of the remaining 3 positions. Thus, as in case 1, the total number of rearrangements in case 2 is 6.
Thus there are 6 + 6, or 12, possible rearrangements, and the correct answer is Choice D.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 11: Divide into Cases
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