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In how many ways can the letters of the word ACCLAIM be rear
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09 May 2019, 01:52
09 May 2019, 01:52
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47% (01:15) correct
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In how many ways can the letters of the word ACCLAIM be rearranged such that the vowels always appear together?
(A) \(\frac{7!}{2!*2!}\)
(B) \(\frac{4!*3!}{2!*2!}\)
(C) \(\frac{4!*3!}{2!}\)
(D) \(\frac{5!}{2!*2!}\)
(E) \(\frac{5!}{2!}*\frac{3!}{2!}\)
(A) \(\frac{7!}{2!*2!}\)
(B) \(\frac{4!*3!}{2!*2!}\)
(C) \(\frac{4!*3!}{2!}\)
(D) \(\frac{5!}{2!*2!}\)
(E) \(\frac{5!}{2!}*\frac{3!}{2!}\)
Re: In how many ways can the letters of the word ACCLAIM be rear
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10 May 2019, 00:42
10 May 2019, 00:42
1
The word "ACCLAIM" has 7 letters so usually words can be arranged as x! where x is the number of letters in the word.
However in this case and in many other words a word contains more than 1 letters that are same such as 2c's and 2A's for Acclaim.
Therefore "ACCLAIM" can be arranged with \(\frac{7!}{2!*2!}\) this is just the arrangement with no constraints.
To get the vowels together let us separate them from other letters. There are 3 vowels in this word. 2A's and 1I. \(7-3 = 4\) letters these are consonants.
Now let us group these vowels together as one. Now we have four letters and 1 group of vowel. Let us consider them together as 5 letters.
Therefore the number of ways in which "ACCLAIM" can be arranged with vowels together is \(\frac{5!}{2!}\). The group of vowels together form a single block so we do not need to account for double A's in the vowel group. But we need to consider a small detail to get to the actual answer. These 3 vowels that we have considered as 1 can interchange places among themselves for eg. AAI and IAA is two different combination. For the final ans we do have to account for 2A's
Hence the ans is \(\frac{5!}{2!}\) * \(\frac{3!}{2!}\)
However in this case and in many other words a word contains more than 1 letters that are same such as 2c's and 2A's for Acclaim.
Therefore "ACCLAIM" can be arranged with \(\frac{7!}{2!*2!}\) this is just the arrangement with no constraints.
To get the vowels together let us separate them from other letters. There are 3 vowels in this word. 2A's and 1I. \(7-3 = 4\) letters these are consonants.
Now let us group these vowels together as one. Now we have four letters and 1 group of vowel. Let us consider them together as 5 letters.
Therefore the number of ways in which "ACCLAIM" can be arranged with vowels together is \(\frac{5!}{2!}\). The group of vowels together form a single block so we do not need to account for double A's in the vowel group. But we need to consider a small detail to get to the actual answer. These 3 vowels that we have considered as 1 can interchange places among themselves for eg. AAI and IAA is two different combination. For the final ans we do have to account for 2A's
Hence the ans is \(\frac{5!}{2!}\) * \(\frac{3!}{2!}\)
Re: In how many ways can the letters of the word ACCLAIM be rear
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24 Oct 2021, 21:18
24 Oct 2021, 21:18
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
