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How many 4letter words can be formed using the alphabets of the word
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Updated on: 07 Aug 2018, 01:06
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How many 4letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4letter word contains alphabets G and L and repetition of alphabets are not allowed? A. \(60\) B. \(120\) C. \(180\) D. \(200\) E. \(240\) Thanks, Saquib Quant Expert eGMATTo read all our articles: Must read articles to reach Q51
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Re: How many 4letter words can be formed using the alphabets of the word
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Updated on: 30 Jan 2017, 23:12



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Re: How many 4letter words can be formed using the alphabets of the word
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30 Jan 2017, 08:53
Is answer C ? We need to select 2 alphabets from E,N,I,S and H, which are arranged also, so 5P2 = 20. We have 3 places so total = 20*3*2*1 = 120;



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Re: How many 4letter words can be formed using the alphabets of the word
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30 Jan 2017, 09:15
EgmatQuantExpert wrote: How many 4letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4letter word contains alphabets G and L and repetition of alphabets are not allowed? A. \(60\) B. \(120\) C. \(180\) D. \(200\) E. \(240\) We have here 7 letters ( E,N,G,L,I,S & H ) And 4 places as _ _ _ _ G & L must be there, so we can arrange the 2 letters in 2! or 2 ways and the next 5 Letters ( E,N,I,S & H ) in 2 places in 5! ways ie, 120 ways... So, Total Number of ways is 120*2 = 240 ways.. Answer must be (E) 240
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Re: How many 4letter words can be formed using the alphabets of the word
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30 Jan 2017, 09:33
EgmatQuantExpert wrote: How many 4letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4letter word contains alphabets G and L and repetition of alphabets are not allowed? A. \(60\) B. \(120\) C. \(180\) D. \(200\) E. \(240\) Thanks, Saquib Quant Expert eGMATHi ankujguptaDo not start arranging the alphabets before selection. Total 7 letters out of which 4 are to be choosen.. G and L are already there, so choose 2 out of remaining 5.. 5C2=\(\frac{5!}{3!2!}=10\).. Now 4 letters can be choosen in 10 ways but they can be arranged in 4! Or 4*3*2=24 ways.. Total 10*24=240.. E
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Re: How many 4letter words can be formed using the alphabets of the word
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30 Jan 2017, 11:27
chetan2u wrote: EgmatQuantExpert wrote: How many 4letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4letter word contains alphabets G and L and repetition of alphabets are not allowed? A. \(60\) B. \(120\) C. \(180\) D. \(200\) E. \(240\) Thanks, Saquib Quant Expert eGMATHi ankujguptaDo not start arranging the alphabets before selection. Total 7 letters out of which 4 are to be choosen.. G and L are already there, so choose 2 out of remaining 5.. 5C2=\(\frac{5!}{3!2!}=10\).. Now 4 letters can be choosen in 10 ways but they can be arranged in 4! Or 4*3*2=24 ways.. Total 10*24=240.. E chetan2u Thanks. Got the error.



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How many 4letter words can be formed using the alphabets of the word
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Updated on: 07 Aug 2018, 02:34
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 The objective of the question is to find the number of 4letter words that can be formed from the alphabets of the word ENGLISH. The information given is: • There are a total of 7 alphabets: E, N, G, L, I, S and H. • Repetition of letters is not allowed. • Two letters G and L are to be included necessarily in all the words. • Per the question, it is not necessary for the word formed to convey a meaning per English dictionary. 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 the following tasks: • Task 1 – Select two letters from the letters G and L. (As these two are to be necessarily included) • Task 2 – Select two letters from E, N, I, S, and H. • Task 3 – Form 4letter words from the four letters that are selected in the previous two tasks.
o Now, in order to accomplish the objective, all the three tasks need to be done. So, in the objective equation, we will put a 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 • Task 1 is to select two letters from the letters G and L.
o Now, the number of ways to select 2 letters from 2 different letters = 2C2 = 1 o Thus, number of ways to do Task 1 = 1 • Task 2 is to select two letters from the 5 letters E, N, I, S, and H.
o The number of ways to select 2 letters from 5 different letters = 5C2 = 10 o Thus, number of ways to do Task 2 = 10 • Task 3 is to arrange the selected 4 letters in 4 spaces to form different words.
o Now, the number of ways in which 4 letters can be arranged in 4 spaces= 4! = 4 X 3 X 2 X 1 o Thus, number of ways to do Task 3 = 24 Step 4: Calculate the final answer • In this step, we are going to plug the values in the above equation:
o Number of different 3letter words = 1 x 10 x 24 = 240 o So, there are 240 words that can be formed per the condition stated in the question.
• Thus, the correct answer choice is Option D. Thanks, Saquib Quant Expert eGMAT
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Re: How many 4letter words can be formed using the alphabets of the word
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30 Jan 2017, 23:12
Method 2 –• Now let us look at another way to solve this question. • We need to make 4 letter words in which G,L must be present . • And the remaining two spaces must be filled with the remaining 5 letters. • Thus, the objective equation can be written as • Thus if we make 4 spaces and try to arrange GL in these 4 spaces, we will clearly see that GL can be arranged in 4P2 ways.
o Thus, the number of ways to arrange GL on 4 spaces = 4P2 = 4!/2! = 12 ways. • To fill the remaining two spaces, we have 5 letters to choose from and arrange them
• Thus, the remaining two spaces can be filled and arranged in = 5P2 = 5!/3! = 20 ways. • Plugging the two values in the objective equation, we get
o The number of ways to make 4 letter words = 12 x 20 = 240 ways. • 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. • Please Note: When we say that G and L must be there in the 4 letter word, it means that they can be placed anywhere in the 4 letter word. And it is NOT necessary to place GL together in the 4 letter word. This is a common mistake, which a lot of students make and one must avoid falling into such a trap! Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
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Re: How many 4letter words can be formed using the alphabets of the word
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