How many 4-letter words can be formed using the alphabets of the word

Question

How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L paired together, with G coming before L and repetition of alphabets being not allowed?

A.  60 
B.  120 
C.  180 
D.  200 
E.  240

Thanks,
Saquib
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EgmatQuantExpert · Accepted Answer

Hey,

PFB the official solution.

This question can be done in a number of ways. Let us focus on the two important methods of solving this question –

Method 1 –

Step 1: Understand the objective

not allowed

occur as a pair and since G comes before L, that means that must always be in the order GL in any word that is formed

So, now we know the objective of the question and the information provided in the question.

Step 2: Write the objective equation enlisting all tasks

The objective comprises of following tasks:

Task 1

Task 2

Task 3

all the three tasks need to be done

multiplication sign between the number of ways of doing the three tasks

The Objective Equation will therefore be:

Step 3: Determine the number of ways of doing each task

number of ways to do Task 1 = 1

number of ways to do Task 2 = 10

number of ways to do Task 3 = 6

Step 4: Calculate the final answer

o Number of different 3-letter words = 1 x 10 x 6 = 60

Option C

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Saquib
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EgmatQuantExpert · Answer

Method 2:

they must be paired together in the order GL

the remaining two spaces must be filled with the remaining 5 letters

the number of ways to arrange GL on 4 spaces = 3 ways

o E, N, I, S, H

the remaining two spaces can be filled and arranged in = 5P2 = 5!/3! = 20 ways

The number of ways to make 4 letter words = 3 x 20 = 60 ways

Option C

As we can see both the methods give us the same answer. In the first method, we first selected the letters and then arranged them and in the second method, we did the selection and arrangement simultaneously.

Thanks,
Saquib
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EgmatQuantExpert · Answer

The official solution has been posted. Looking forward to a healthy discussion..

ravisinghal · Answer

out of 7 letters 2 are confirmed.Rest two can be taken in 5c2 ways

total words :- 5c2*3! = 60..answer A

monish447 · Answer

out of the 4 options, two consecutive places have been fixed. Number of ways of doing this for G and L = 3
since two alphabets out of 7 have been used, we have 5 options left for the 2 left places. Hence 5 X 4 (without repetition)
Ans = 3*(4*5) = 60

Popyes26 · Answer

I am not sure of this question.. can someone explain to me why "with G coming before L" only means that "G" is  exactly  before "L" as per the OA.

Because the way I understood the question is, when G comes before L.. the solution can be "GxxL", "GxLx", etc., and accordingly the answer should be 120.

EMPOWERgmatRichC · Answer

Hi All,

To start, this question is really poorly-worded, but the math behind it is just "Permutation math." There are a number of different ways to approach it - and even if you don't know how to do all of the math "all at once", you can still solve it by breaking the calculation down into pieces.

We're asked for the number of 4-letter words that can be formed using the letters in the word ENGLISH, with the following restrictions: 
1) The letters G and L must be in the word 
2) The G must appear before the L (the intent of this restriction is that the G must appear IMMEDIATELY BEFORE the L, although the way the prompt is written is vague on this particular point). 
3) Letter repetition is NOT allowed.

Since we MUST use the G and the L, we're going to choose 2 additional letters from the 5 remaining letters (E, N, I, S and H). Since the G must come 'immediately before' the L, we can 'map out' the various ways that that can happen:

1st option: G L _ _

Here, the first blank would be filled by one of the 5 other letters (and once we choose a letter, the second blank would be filled with one of the 4 remaining letters). Thus, there are (5)(4) = 20 words that begin with "GL"

From here, we just have to account for all of the ways that the L can immediately follow the G: 
G L _ _ 
_ G L _ 
_ _ G L

Each of these 3 possibilities would have 20 options each... (3)(20) = 60 possible words

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

Let’s first calculate the number of words of the form G - L - _ - _. For the first blank, there are five choices (any one of the letters E, N, I, S or H) and for the second blank, there are four choices. Thus, there are 5 x 4 = 20 words of this form.

Next, we notice that the words can also be of the form _ - G - L - _ or _ - _ - G - L. The number of different words is 20 for each form. Thus, there are 20 + 20 + 20 = 60 possible words in total.

Answer: A

Kinshook · Answer

Asked: How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L paired together, with G coming before L and repetition of alphabets being not allowed?

Let us form a single letter by combining GL together.
Now we have to form 3-letter words with GL as a letter.
There are 5 more letters in ENGLISH other than G & L, out of which 2 are to be selected

Number of ways = 5C2 * 3! = 10 *6 = 60

IMO A

sayan640 · Answer

With G and L thought as one entity , we can arrange the other two numbers in 5*4 ways i.e 20 ways.
For each of these ways , (GL) , _ , _ numbers can be arranged in 3! ways . Hence all the numbers can be arranged in 20 * 3! ways .
But G will always be ahead of L ,hence divide it by 2 . Hence the ans is 120/2 = 60
 MartyMurray   KarishmaB

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How many 4-letter words can be formed using the alphabets of the word

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