Note 5 at Mk. 16:8: Mark says that these women were so afraid that they didn't say anything to anyone. Matthew implies that these women told the disciples of what they had seen (Mt. 28:8) and Luke clearly states that they told the apostles and that the apostles didn't believe them.

The simplest harmony between these accounts would be that they didn't tell anyone except the apostles and that is what Mark meant. It is also possible that because of their fear they didn't tell the apostles at first. Then, after Mary Magdalene came and told of seeing Jesus (see note 5 at Lk. 24:10, p. 487), they could have verified her story by sharing what they had seen and heard.

The most probable explanation, based on the context (Mt. 28:10), is that when they left the tomb they were so frightened that they intended not to tell anyone. However, after Jesus appeared to them, their joy replaced their fear and they rushed to tell the apostles.

At any rate, solutions to this apparent contradiction exist and can be explained as simply one writer providing more or less detail than the others.