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QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink]
 12 Sep 2016, 12:16
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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 ? A. 60 B. 36 C. 24 D. 12 E. 6 Practice Questions
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Re: QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink]
12 Sep 2016, 12:18
ExplanationWhen 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.
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Re: QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink]
20 Sep 2016, 05:53
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sandy wrote: 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
A. 60
B. 36
C. 24
D. 12
E. 6
Another approach: Take the task of arranging the 7 digits and break it into stages. We’ll begin with the most restrictive stages. Stage 1: Place the letter G Since the letter G must be placed in the 3rd position, we can complete stage 1 in 1 way Stage 2: Place the letter H So far we have: _ _ G _ _ Since H cannot be next to G, we can only place H in the 1st position or the 5th position So we can complete this stage in 2 ways. Stage 3: Place the letter I We can place I wherever we wish. There are 3 spaces remaining, so we can complete this stage in 3 ways. Stage 4: Place the letter J We can place I wherever we wish. There are 2 spaces remaining, so we can complete this stage in 2 ways. Stage 5: Place the letter K There is 1 space remaining, so we can complete this stage in 1 way. By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus arrange all 5 letters) in (1)(2)(3)(2)(1) ways (= 12 ways) Answer: D Cheers, Brent
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Re: QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink]
27 Jul 2018, 02:17
sandy wrote: Explanation
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. @sandy why can't we do like this 1] total no of arrangements 5!=120 2] then place H in 2nd and 4th position, so no of ways are 12 3] then subtract 120-12 = 108 why is this approach wrong?
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Re: QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink]
27 Jul 2018, 06:53
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ssp4all wrote: @sandy why can't we do like this
1] total no of arrangements 5!=120
2] then place H in 2nd and 4th position, so no of ways are 12
3] then subtract 120-12 = 108
why is this approach wrong? G is not in the third place in your assumption. If G is in third place 1. total number of arrangements 4!=24 (Not 5! as G is fixed to 3rd place)2] then place H in 2nd and 4th position, so no of ways are 12 3] then subtract 24-12 = 12 Now its OK
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Re: QOTD#19 The 5 letters in the list G, H, I, J, K are to be
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