Question 410007
here total 12 letters...

no. of t = 2

no. of r = 2 

no. of o = 2

and others are single.

  No. of different vowels = 3 (i,o and e)

no. of ways to arrange 11 letters when 'I' at first place =  11!/ [2! * 2! * 2!]

= 4989600


no. of ways to arrange 11 letters when 'O' at first place =  11!/ [2! * 2! ] 

= 9979200

no. of ways when 'E' at first place = 11!/ [2! * 2! * 2!]

= 4989600



total no. of ways when vowel at the first letter = 4989600 + 9979200 + 4989600

= 19958400




try to understand the concept and solve it yourself....