In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?
Question and options
In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?
- 75600
- 25200
- 37800
- 21600
Answer and explanation
Correct answer: C - 37800
MANAGEMENT: consonants M,M,N,N,G,T (6), vowels A,A,E,E (4). Arrange consonants 6!/(2!2!)=180, choose 4 of 7 gaps C(7,4)=35, arrange vowels 4!/(2!2!)=6. Total 180*35*6=37800.
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