How many ways can the letters of the word, ‘MACHINE’ be arranged so that the vowels may occupy only the odd positions? Pick one
A) 210  B) 576  C) 144  D) 456  E) 356
In the word ‘MACHINE’ 3 vowels and 4 consonants.   v v v v   __ _ __ _ __ _ __   Now, 3 vowels can be placed at any of 3 places, out of which 4 marked 1,3,5,7.   Number of ways arranging the vowels= 4P3 = (4*3*2)= 
<gadget id="calculator">(4*3*2)</gadget>
<output>24</output>
24   Also, 4 consonants at the remaining 4 positions may be arranged in= 4P4 = 4!= 24 ways.   Therefore, Required number of ways= (24*24)= 
<gadget id="calculator">(24*24)</gadget>
<output>576</output>
576.   ANSWER:576
<result>B</result>
How many ways can the letters of the word, ‘MACHINE’ be arranged so that the vowels may occupy only the odd positions?