In how many ways can the letters of the word ACCLAIM be rearranged suc

Question

In how many ways can the letters of the word ACCLAIM be rearranged such that the vowels always appear together?

(A) 7!/(2!2!)

(B) 4!3!/(2!2!)

(C) 4!3!/2!

(D) 5!/(2!2!)

(E) 5!/2!*3!/2!

Lampard42 · Answer

Total letters = 7. Vowels =3 with one letter repeated twice and non vowels =4 with one letters repeated twice. Assume all vowels as one word so no. Of possible arrangements is 5!/2! And vowels can between them be arranged by 3!/2!. So option E

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Archit3110 · Answer

ACCLAIM
Consonants ; 5 arranged ; 5!/2!
Vowels 3 ; arrraged ; 3!/2!
total ways 5!/2! * 3!/2!
IMO E

eswarchethu135 · Answer

AAI and CCLM are 2 units here. The condition is on AAI, that these should always appear together. This can be done in 5! ways (4 consonants + 1 unit of all vowels).

Consonants can be arranged in  \frac{5!}{2!}  ways. Vowel unit can be arranged in  \frac{3!}{2!}  ways.

Total =  \frac{5!}{2!}*\frac{3!}{2!}

OPTION:  E

alessandrosolaro · Answer

MathRevolution · Answer

The given word is 'ACCLAIM'

Condition: Vowels together

=> CCLM (AAI) - Total we have 5 things to arrange which can be done in 5! ways * '3' vowels can be arranged in 3! ways

=> 'C' is repeating itself twice and so does 'A'. Therefore,

Total arrangements:  \frac{(5! * 3!)}{(2! * 2!)}

Answer E

CEdward · Answer

Tough permutation problem.

In the absence of repeats we're looking at:

7! / 2! = 2520 different ways the letters can be rearranged, but this includes permutations that we don't want

Group some the vowels together into 1

5! / 2! <--- 2! is the repeat Cs

The vowels can be rearranged in 3!/2 ways

5! / 2! x 3!/2

Answer is E.

luisdicampo · Answer

Deconstructing the Question  
The word is  ACCLAIM  (7 letters).
Vowels: A, A, I (3 vowels).
We are told that the vowels must always appear together.

Step-by-step  
Treat the 3 vowels as one block.

Now we have:
Vowel block + C + C + L + M
Total objects = 5, with C repeated twice.

Number of external permutations:
 5! / 2!

Internal permutations of vowels (A, A, I):
 3! / 2!

Multiply:
 (5!/2!) × (3!/2!) = 5!·3! / (2!·2!)

Answer: E

In how many ways can the letters of the word ACCLAIM be rearranged suc

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GMAT Problem Solving (PS) Questions

In how many ways can the letters of the word ACCLAIM be rearranged suc

Prep Toolkit

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