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How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word

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by BTGmoderatorDC » Sun Mar 15, 2020 4:47 pm

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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



OA A

Source: e-GMAT
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Re: How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word

by Jay@ManhattanReview » Sun Mar 15, 2020 9:39 pm
BTGmoderatorDC wrote: ↑
Sun Mar 15, 2020 4:47 pm
 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

OA A

Source: e-GMAT
The word ENGLISH has 7 letters and we have to select 4 letters to form words such that the letters G and L are among the selected letters. moreover, G and L are paired together.

Since the letters G and L are paired together, let's consider them as one letter. So, we have 7 – 2 = 5 letters, and now we have to select 4 – 2 = 2 letters.

Thus, # of ways to select 2 letters out of 5 letters = 5C2 = 10 ways

# of possible arrangements(4-letter words) out of 3 letters = 3!*10 = 6*10 = 60

The correct answer: A

Hope this helps!

-Jay
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Re: How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word

by Scott@TargetTestPrep » Wed Mar 18, 2020 3:52 pm
BTGmoderatorDC wrote: ↑
Sun Mar 15, 2020 4:47 pm
 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



OA A

Source: e-GMAT
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

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