Question
Find the number of ways to arrange each letter of the
word 'COMMITTEE' such that all the vowels always come together.Solution
Take all the vowels (OIEE) as one entity.
Number of letters now = 5 + 1 = 6!
Number of ways to arrange all the letters = 6! ÷ (2! × 2!) = 720 ÷ 4 = 180
Number of ways to arrange vowels = 4! ÷ 2! = 24 ÷ 2 = 12
Required number of ways = 180 × 12 = 2,160
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