Question 396688: 1. how many different ways can the letters "SIMILAR" be arranged if letter "I" must be first letter?
2. how many different ways can the letters "TRIGONOMETRY" be arranged if a vowel must be first letter?
Answer by sudhanshu_kmr(1152)   (Show Source):
You can put this solution on YOUR website!
1. there are total 7 letters, letter I is two times..
after putting the I on first place we have remaining 6 letters i.e SMILAR
total no. of ways to arrange 6 letters = 6! = 720
2.
here 3 vowels, i.e I, O and E . after putting vowel of first place we have remaining 11 letters..
when I on first place , number of ways = 11!/( 2! * 2! * 2!) = 4989600
when O on first place, number of ways = 11! / ( 2! * 2!) = 9979200
when E on first place, number of ways = 11!/( 2! * 2! * 2!) = 4989600
total no. of ways = 19958400
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