Question
Find the number of ways to arrange each letter of the
word 'RECREATION' such that all the vowels always come together.Solution
Number of letters = 10
Take all the vowels (EEAIO) as one entity.
Number of letters now = 5 + 1 = 6!
Number of ways to arrange all the letters = 6! ÷ 2! = 720 ÷ 2 = 360
Number of ways to arrange vowels = 5! ÷ 2! = 120 ÷ 2 = 60
Required number of ways = 360 × 60 = 21,600
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