SOLUTION: In how many different ways can the letters of the word “trigonometry” be arranged if a vowel must be the first letter of each permutation?

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Question 410007: In how many different ways can the letters of the word “trigonometry” be arranged if a vowel must be the first letter of each permutation?
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!
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....