In how many different ways can the letters of the word ATRIUMS be arranged in such a way that the vowels occupy only the even positions?
Choose the correct choice from the following options.
A) 72 B) 96 C) 120 D) 144 E) 180
The 3 vowels can be arranged in 3 even places in 3! ways.   The 4 consonants can be arranged in 4 odd places in 4! ways.   The number of arrangements with vowels in even positions = 3! Ã— 4! = 6 Ã— 24 = 144   The answer is 144.
<result>D</result>
In how many different ways can the letters of the word ATRIUMS be arranged in such a way that the vowels occupy only the even positions?