Solution. We begin by considering RFRNC

We begin by considering RFRNC. The number of arrangements of these letters is since the two R’s are indistinguishable.

Again considering one possible arrangement of the letters, say RFNRC, the positions that the three E’s can take are shown below.

We need to find the number of combinations of four from six positions, which is

Hence the number of arrangements where the E’s are separated is