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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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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 Gmat_mission » Thu Dec 17, 2020 12:42 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 and repetition of alphabets are not allowed?

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

Answer: E

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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 Dec 23, 2020 4:19 pm
Gmat_mission wrote: ↑
Thu Dec 17, 2020 12:42 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 and repetition of alphabets are not allowed?

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

Answer: E

Solution:

Let’s first calculate the number of ways we can choose the letters. Since the word must include G and L, we need to choose two letters from among the remaining letters (which are E, N, I, S or H). There are 5C2 = 5!/(2!*3!) = 10 ways to make this choice.

Once the four letters to make up the word are determined, we note that there are 4! = 24 ways to arrange these letters. Thus, there are 24 * 10 = 240 words which contain G and L.

Answer: E

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