Question

in how many different ways letters of the word manpower be arranged such that all vowels are together​

Answer 1

Answer:

Vowels=a, o, e

Total=8

Total number of arrangements =6!*3!=720*6=4320

Answer 2

60 different ways letters of the word MANPOWER be arranged such that all vowel are together.

Given that,

We have to find how many different ways letters of the word MANPOWER be arranged such that all vowel are together.

We know that,

The word MANPOWER has 11 letters out of which 5 are consonants (MNPWR) and 3 are vowels (AOE)

Considering the objects of the same type, the number of arrangements of these vowels will be 3!/3! =1

Since, the vowels have to  be together, we say that we have to arrange the groups (M), (N),(P),(W),(R) and (AOE) among themselves.

Considering the objects of same type, this can be done in 5!/2! = 60 ways

And, The total number of arrangements all the letters = [ number of arrangements of (M), (N),(P),(W),(R) and (AOE)] × [number of arrangements of (AOE)]

=1×60 = 60 ways.

Therefore, 60 different ways letters of the work MANPOWER be arranged such that all vowel are together.

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