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In how many ways can the letters of the word ACUMEN be rearr
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09 May 2019, 01:45
09 May 2019, 01:45
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Question Stats:
55% (00:44) correct
45% (00:57) wrong based on 20 sessions
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In how many ways can the letters of the word ACUMEN be rearranged such that the vowels always appear together?
(A) \(3!*3\)!
(B) \(\frac{6!}{2!}\)
(C) \(\frac{4!*3!}{2!}\)
(D) \(4!*3!\)
(E) \(\frac{3!*3!}{2!}\)
(A) \(3!*3\)!
(B) \(\frac{6!}{2!}\)
(C) \(\frac{4!*3!}{2!}\)
(D) \(4!*3!\)
(E) \(\frac{3!*3!}{2!}\)
Re: In how many ways can the letters of the word ACUMEN be rearr
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10 May 2019, 00:47
10 May 2019, 00:47
1
For ACUMEN there are 6 letters. Of these A, U, E are vowels. There are 3 vowels.
There are 3 consonants and 3 vowels. Let us group the vowels together as one element.
We will arrange 4 elements 3 consonants and 1 group of vowel as another element.
Therefore these letters can be arranged as 4!* 3!. Where 3! is for interchanging places between the vowels themselves.
For eg. one arrangement could be CMNAUE and another could be CMNUEA
There are 3 consonants and 3 vowels. Let us group the vowels together as one element.
We will arrange 4 elements 3 consonants and 1 group of vowel as another element.
Therefore these letters can be arranged as 4!* 3!. Where 3! is for interchanging places between the vowels themselves.
For eg. one arrangement could be CMNAUE and another could be CMNUEA
Re: In how many ways can the letters of the word ACUMEN be rearr
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06 Oct 2019, 14:50
06 Oct 2019, 14:50
What if the word is "MATHEMATICS" or "PARALLEL"?
