Question
Find the number of ways to arrange each letter of the
word 'AGRICULTURE' such that all the vowels always come together.Solution
Number of letters = 11
Take all the vowels (AIUUE) as one entity.
Number of letters now = 6 + 1 = 7!
Number of ways to arrange all the letters = 7! ÷ 2! = 5040 ÷ 2 = 2,520
Number of ways to arrange vowels = 5! ÷ 2! = 120 ÷ 2 = 60
Required number of ways = 2,520 × 60 = 1,51,200
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