Jamboree and GMAT Club Contest Starts
QUESTION #12:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together? Choose the correct choice from the following answers
A) 660	B) 600	C) 400	D) 300	E) 240
The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.   Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together   In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,   Total arrangements = 6!/2!   Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.   Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.   Hence, Arrangements when two E’s are together = 5! * (2!/2!)   Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2= 
<gadget id="calculator">120 * 2</gadget>
<output>240</output>
240.   Option 400 is correct!
<result>C</result>
Jamboree and GMAT Club Contest Starts
QUESTION #12:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?