Maths · Simple applications
The number of words that can be formed out of the letters of the word "ARTICLE"
The number of words that can be formed out of the letters of the word "ARTICLE" so that the vowels occupy even places is
- A. 574
- B. 36
- C. 754 \)
- D. 144
Step-by-step solution
The word 'ARTICLE' has 7 letters: vowels A, I, E (3) and consonants R, T, C, L (4). Even positions are 2, 4, 6. Vowels must occupy these 3 positions: 3! = 6 ways. Consonants occupy remaining 4 odd positions: 4! = 24 ways. Total words = 6 × 24 = 144.
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