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

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AAPL: Moderator; Posts: 2632; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Tue Dec 11, 2018 4:59 am

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e-GMAT

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

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Source: Beat The GMAT — Problem Solving | Tue Dec 11, 2018 4:59 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Dec 11, 2018 10:09 pm

AAPL wrote:e-GMAT

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

The word ENGLISH has 7 alphabets with no alphabet being repeated.

Since the two alphabets, G and L are already chosen, we are left with only two alphabets to be chosen.

The number of ways to select two alphabets = 5C2 = 5.4 / 1.2 = 10

Let club G and L as one alphabet.

So, we have three alphabets: (G&L, and two others)

# of 4-letter words contains alphabets G and L paired together = 3P3 * 10 = 3!*10 = 6*10 = 60 words.

The correct answer: A

Hope this helps!

-Jay
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