Question

​In ​how ​many ​ways ​can ​the ​7 ​letters ​A,B,C,D,E,F ​and ​G ​be ​arranged ​so ​that ​C ​and ​E ​never together.

Answer 1

We first arrange all the letters beside C and E. In the 6 spaces generated we choose 2 and arrange C and E in them. Since, we put them in the generated gaps this ensures there is always at leat 1 letter between them