Latest CTS Aptitude Question SOLUTION: In how many ways can the letters of the word ACUMEN be rearranged such that the vowels alwaysappear together?

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In how many ways can the letters of the word ACUMEN be rearranged such that the vowels alwaysappear together?

Asked In CTS varma (11 years ago)

Solved chaitanya Read Solution (9)

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Read Solution (9) :

chaitanya  (11 years ago)

The word “rearranged” indicates that this is a permutation problem.

The base set {A, C, U, M, E, N} has no indistinguishable objects.

Repetition is not allowed.

Since the 3 vowels must appear together, treat the three as an inseparable unit. Hence, reduce the base set to{{A, U, E}, C, M, N}.

Now, there are 4 different units in the base set, and they can be arranged in
4P4= 4!ways.

The unit {A, U, E} can itself be internally arranged in
3P3= 3! ways.

Hence, by The FundamentalPrinciple of Counting, the total number of ways of arranging the word is 4!x 3!.

Is this solution Helpfull? Yes (47) | No (7)  

Aman  (11 years ago)

ACUMEN
AUE will come together as a group which can be arranged in 3!=6 ways.
AUE, C,M,N can be arranged in 4!=24 ways.

total possible arrangements = 24*6=144 ways

Is this solution Helpfull? Yes (22) | No (3)  

Dipannita  (11 years ago)

A,C,U is taken as one letter
hence there are 4 letters and the 3 vowels can arrange among themselves in 3! ways
Hence ans is 4!*3!=144

Is this solution Helpfull? Yes (6) | No (1)  

aanchal sharma  (11 years ago)

4!*3!=144
there are three constants and three vowels,three vowels always comes together so total number of words are 4.and three vowels can be arranged in 3! ways.

Is this solution Helpfull? Yes (3) | No (1)  

lilesh  (10 years ago)

here we are asked for rearrangement ,it means that it is already arranged once so the answer will be (4!-3!)-1=143

Is this solution Helpfull? Yes (2) | No (1)  

Gayathri Muthraman  (11 years ago)

vowels together rules:
1)take out vowels from given letter, count the rest and add 1, find facto
2)find facto for vowels and multiply the result with (1)
so ans is:
ACUMEN => CMN(AEU)=> now totally 4,so 4!=>24
now for vowels AEU=>3!=>6
24*6=144

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preethi v v   (10 years ago)

ans is 4!*3!=144

Is this solution Helpfull? Yes (1) | No   

ASHISH KUMAR  (10 years ago)

4!*3! as we have to assign vowels together so we hv left wid 4 groups..arranging 4 together is 4! nd 3 letters can also b arranged in 3! ways

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G.Mounika  (7 years ago)

vowels are A U E so we unite them and remaining 3 letters and vowels together we have 4 units so we can arrange 4! and vowels can be arranged in 3! ways so we can arrange in 4!*3!= 144 ways

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