In how many ways can the letters of the word, ‘LANGUAGE’ be arranged in such a way that the vowels always come together?
Pick:
A) 600 B) 700 C) 720 D) 750 E) 780
In the word ‘LANGUAGE’ we treat the vowels AUAE as one letter. Thus, we have LNGG (AUAE).   This we have 5 letters of which G occurs 2 times and the rest are different.   Number of ways arranging these letters= 5!/2! =5*4*3= 
<gadget id="calculator">5*4*3</gadget>
<output>60</output>
60   Now, 4 letters of which A occurs 2 times and the rest are different, can be arranged in 4!/2!= 4*3= 
<gadget id="calculator">4*3</gadget>
<output>12</output>
12.   Therefore, Required number of ways= 60*12= 
<gadget id="calculator">60*12</gadget>
<output>720</output>
720   ANSWER: 720
<result>C</result>
In how many ways can the letters of the word, ‘LANGUAGE’ be arranged in such a way that the vowels always come together?