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