Question

Find the number of words that can be formed by taking all the letters of the word “COMBINE”, such that the vowels occupy odd places.

Answer 1

There are 7 letters in the word COMBINE of which 4 are consonants and 3 are vowels (O, I, E). 

There are 4 odd places in a 7 letter word, so the number of ways 3 vowels can be arranged in 4 places = ⁴P₃ 

After arranging the 3 vowels, there are 4 places left (one at odd position and 3 at even positions). So the 4 consonants can be arranged in these 4 places in 4! ways. 

∴ Required number of words = ⁴P₃ × 4! = 4 × 4 × 3 × 2 × 1 = 96.