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QOTD#19 The 5 letters in the list G, H, I, J, K are to be

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GMAT Club Legend
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Joined: 07 Jun 2014
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QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink] New post 12 Sep 2016, 12:16
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Question Stats:

75% (00:43) correct 25% (01:47) wrong based on 12 sessions
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

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Question: 14
Page: 206
[Reveal] Spoiler: OA

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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

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Re: QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink] New post 12 Sep 2016, 12:18
Expert's post
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.
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Re: QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink] New post 20 Sep 2016, 05:53
Expert's post
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] New post 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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GMAT Club Legend
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Kudos [?]: 1612 [1] , given: 375

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Re: QOTD#19 The 5 letters in the list G, H, I, J, K are to be [#permalink] New post 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   [#permalink] 27 Jul 2018, 06:53
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