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`        In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?`
6 years ago

Sudheesh Singanamalla
114 Points
```										ABACUS
vowels = AAU = 3 vowels.
number of letters = 6
let us take the vowels as one.
so number of letters now = 4
number of ways in which vowels occur together = 4! = 4*3*2*1=24
but the vowels can also be shifted in 3! ways = 3*2*1 = 6
so total ways in which vowels occur together = 6*24 = 144

so the answer is 144 ways.

```
6 years ago
parth pankaj tiwary
18 Points
```										you can assume AAU as only one element and can find the number of ways easily.............
```
6 years ago
SHUBHRANSHU KUMAR
19 Points
```										there are six words in abacus
take vowels a single unit AAU=1WORD
SO THERE ARE NOW 4 WORDS AND THEY CAN BE ARRANGED IN  4*3*2*1 =24 WAYS.
BUT THERE ARE THREE VOWELS THAT CAN BE ARRANGED IN 3*2*1/2* =3 WAYS  AS THERE ARE TWO SAME VOWELS AA.
SO TOTAL WAYS ARE   72.
```
6 years ago
15 Points
```										let us assume AAU = X
now we have to arrange XBCS
dis can be done in 4! ways... 4!=24
now AAU cn be arranged in 3 ways...
so answer vil be 24*3 = 72.
```
6 years ago
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