Question
Find the number of ways to arrange each letter of the
word 'PROFESSION' such that all the vowels always come together.Solution
Number of letters = 10
Take all the vowels (OEIO) as one entity.
Number of letters now = 6 + 1 = 7!
Number of ways to arrange all the letters = 7! Ă· 2! = 5040 Ă· 2 = 2,520
Number of ways to arrange vowels = 4! Ă· 2! = 24 Ă· 2 = 12
Required number of ways = 2,520 Ă— 12 = 30,240
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