The letters of the word ‘RANDOM’ are arranged in all possible ways. The number of arrangements in which there are 2 letters between R and D is

Two letters can be selected from $4\left(A,N,O,M\right)$ in ${}^4{p}_2=12$ ways

By treating $R--D$ as one unit the no of arrangement are $3!$  ways

R&D among them selves can be arranged in $2!$  ways

$\therefore$  The number of arrangements in which there are 2 letters between R and D is ${=}^4{P}_2.3!.2!=144$