(a) The word RELEASED consists of 8 letters where E is repeated twice. The number of different arrangements is given by \(\frac{8!}{2!}\). Calculating this gives \(\frac{40320}{2} = 6720\).

(b) Treat LED as a single unit. This gives us 6 units to arrange: LED, R, E, A, S, E. The number of arrangements is \(\frac{6!}{2!}\) because E is repeated. Calculating this gives \(\frac{720}{2} = 360\).

(c) First, calculate the total number of arrangements where A and D are together. Treat AD as a single unit, giving us 7 units: AD, R, E, L, E, S, E. The number of arrangements is \(\frac{7!}{3!}\) because E is repeated. Calculating this gives \(\frac{5040}{6} = 840\). The probability that A and D are not together is \(1 - \frac{840}{6720} = \frac{3}{4}\) or 0.75.