Answer to Question #184900 in Statistics and Probability for Zzesk

Question

How many arrangements are possible for the word GROVEL if the vowels

are always together?

Answer 1

Grovel has two vowels.

Grouping the vowels together OEGRVL

Let the grouped vowels be represented by X

OEGRVL=>XGRVL

We have a 5 lettered word. The number of arrangements is 5P5=5!

But again we have 2 vowels which can take various arrangements within themselves. The number of arrangements within the vowels are 2P2=2!

The total number of possible arrangements are

5!*2!=120*2

=240