In how many ways can the letters of a word 'ENGINEERING' be arranged such that vowels DO NOT together?	Choices:	A) 253000	B) 263000	C) 273000	D) 283000	E) 293000
ENGINEERING   total 11 letters   E=3,N=3,G=2,I=2,R=1,   Total no. of ways = 11!/3!3!2!2! = 277200   when vowels come together = (EEEII)NNNGGR =&gt; 7!/3!2! * 5!/3!2! = 4200   No. of ways when vowels DO NOT together = 277200 - 4200= 
<gadget id="calculator">277200 - 4200</gadget>
<output>273_000</output>
273000   ANSWER:273000
<result>C</result>
In how many ways can the letters of a word 'ENGINEERING' be arranged such that vowels DO NOT together?