# How many arrangements of the letters in the word GRACIOUS both begin and end w/ a vowel?

##### 1 Answer

Feb 28, 2016

#### Explanation:

There are 4 options for vowels which may be in the first or last position hence we need to know in how many ways can you choose 2 from an available 4 and arrange them.

This is equivalent to solving the permutation

However, for each of these 12 ways in which 2 vowels can be chosen for the first and last letter, the remaining 6 letters not chosen can be chosen and arranged in

Hence, by the multiplication principle, the total number of different ways that the letters can be arranged subject to the given constraints is