How many strings can be formed from the word ARTICLE

Question

How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?

Answer 1

ARTICLE

Vowels A, I, E = 3

Total number of places = 7

1 2 3 4 5 6 7

Number of even places = 3

3 Vowels can occupy 3 places in 3! = 3 × 2 × 1 = 6 ways

Then the remaining 4 letters can be arranged in 4! ways

So total number of arrangement = 3! × 4! = 6 × 24 = 144 ways