How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?	Select:  A) 9  B) 15  C) 32  D) 56  E) 72
Sol. The given word contains 5 different letters.   Taking the vowels EA together, we treat them as one letter.   Then, the letters to be arranged are XTR (EA).   These letters can be arranged in 4! = 24 ways.   The vowels EA may be arranged amongst themselves in 2! = 2 ways.   Number of words, each having vowels together = (24x2) = 48 ways.   Total number of words formed by using all the letters of the given words   = 5! = (5x4x3x2x1) = 120.   Number of words, each having vowels never together = (120-48)= 
<gadget id="calculator">(120-48)</gadget>
<output>72</output>
72.   Ans: 72
<result>E</result>
How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?