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#

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#