# How many ways can you arrange the letters from the word HAMILTON if you want the arrangement to begin with a vowel still no repeating?

$15120$

#### Explanation:

Given word: HAMILTON

The above word has three vowels A, I \ & \ O & five consonants $H , L , M , N , T$

The first (leftmost) place of each word begins with a vowel hence the number of ways of filling first place of each word

$= 3$

And the number of ways of filling rest $7$ places of each word

=7!

hence, total number of words beginning with a vowel

=3\times 7!

$= 15120$