In how many ways the word ENGINEERING can be arranged so that no vowel come together???	Choose the correct choice from the following options.
A) 273000
B) 283000
C) 293000
D) 263000
E) 253000
Total no. of ways ENGINEERING can be arranged is   E=3, N=3, G=2, I=2, R=1   =&gt; 11!/(3!*3!*2!*2!) =&gt; 277200   No. of ways vowels come together   Vowels ==&gt; (eieei)ngnrng =&gt;   eieei can be considered as 1 letter ... so 1!   ngnrng = 6!   eieei can be arranged as 5!/(3!*2!)   ngnrng can be arranged as 6!/(3!*2!)   So (1!+6 !)*5!/(3!*2!*3!*2!)   =&gt; 4200   So no. of ways vowels not come together   =&gt; 277200 - 4200= 
<gadget id="calculator">277200 - 4200</gadget>
<output>273_000</output>
273000   273000NSWER:273000
<result>A</result>
In how many ways the word ENGINEERING can be arranged so that no vowel come together???