How many possible arrangments are there of the letters A,B,C,D,E,F in which E and F are not next to eachother?

Answer 1

with no restriction there would be 6! or 720 ways

the no of ways in which the E and F are together = 2(5!) ways or 240

so the number of ways the E and F are apart are 720 - 240 or
480 ways.