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

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.

Please approve.

Approved

you can assume AAU as only one element and can find the number of ways easily.............

Approved

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.

Approved

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.

Approved