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?

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Answer 1 · 2018-07-12T22:54:13

$15120$ $15120$

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

$=3\times 7!$

$=15120$