In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?
Select the correct option:
A) 36
B) 48
C) 72
D) 96
E) 128
total number of ways to arrange all the letters = 5!/2!   this includes when both I's are together and not together.   now consider both I's are combined together and arranged, then total number = 4!   these are the arrangements when both the I's are together.   so number of ways when both I's are not together = 5!/2! - 4! = 60-24= 
<gadget id="calculator">60-24</gadget>
<output>36</output>
36   36nswer:36
<result>A</result>
In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?