# Find the number of arrangements of the letters of the word REPUBLIC. How many arrangements start with a vowel ?

There are 8 letters in the word REPUBLIC and all of them are distinct.
Total number of arrangements = 8!

There are three vowels that are E, U and I.
Starting with E, the remaining 7 letters can be arranged in 7! ways.
Starting with U, the remaining 7 letters can be arranged in 7! ways.
Starting with I, the remaining 7 letters can be arranged in 7! ways.
so total no. of arrangements = 7! + 7! + 7! = 3 (7!)

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