How many different ways are possible to arrange the letters of the word “MACHINE” so that the vowels may occupy only the odd positions?
Choose the correct option:
A) 800  B) 125  C) 348  D) 576  E) None of these
Solution   MACHINE has 4 consonants and 3 vowels.The vowels can be placed in position no. 1, 3, 5, 7   ⇒ Total number of ways possible = 4P3 = 24.   For each of these 24 ways the 4 consonants can occupy the other 4 places in 4P4 ways   ⇒ Total = 24 × 24 = 576. Answer 576
<result>D</result>
How many different ways are possible to arrange the letters of the word “MACHINE” so that the vowels may occupy only the odd positions?