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

Question

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

chetan2u · Accepted Answer

Letters... _ _ G _ _
Total ways to fit in 4 ways = 4!
Let H and G be together...
1) let H be prior to G
 _ H G _ _ - 3 places can be placed in 3! = 6 ways
2) Let H be after G
_ _ G H _ -- 3 places can be filled in 3! Ways
Total ways H and G are together = 6+6=12

Ans =24-12=12

D

DavidTutorexamPAL · Answer

As the calculation we're asked to do is relatively straightforward, we'll just do it.
This is a Precise approach.

We have 2 possible locations to place H (1st or 5th), 1 possible location to put G (3rd) and then need to divide the other 3 letters in the remaining 3 places.
This gives 2*1*3! = 2*6 = 12 possible options.

(D) is our answer.

theSachin · Answer

We have two case here...when h is at first place and when h is at second place 
H at first place=6 ways
H at second place = 6 ways 
Total= 12 ways 
So...ans is D

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MathRevolution · Answer

We have 5 letters: G, H, I J, and K.

Condition 1: G at  3^{rd}  place. ( There is only one way we can place G = 1!)
Condition 2: H is not next to G ( H can be placed at  1^{st}  or  5^{th}  position = 2!)

Remaining three letters I, J and K can be arranged in 3! ways.

Overall ways: 1! *2! *3! = 12 ways.

Answer D

KarishmaB · Answer

Simply use the fundamental counting principle discussed in video here: https://www.youtube.com/watch?v=LFnLKx06EMU and blog post here: https://anaprep.com/combinatorics-basic ... angements/ G's place is fixed: ___ ____ G ____ ____ H must be placed at either the 1st or the 5th spots i.e. there are 2 spots for H. Rest of the 3 letters will be arranged in 3 spots in 3! ways Total arrangements = 2 * 3! = 12 Answer (D)

bumpbot · Answer

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

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

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