This Bible contradiction is from the Skeptic's Annotated Bible.
Only the followers of Jesus can do it. (It's one of the signs of a true believer.)
Mark 16:17 View context
And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues;
Others can do it, too.
Matthew 7:21-23 View context
Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.
Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works?
And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
Mark 9:38 View context
And John answered him, saying, Master, we saw one casting out devils in thy name, and he followeth not us: and we forbad him, because he followeth not us.
Luke 9:49 View context
And John answered and said, Master, we saw one casting out devils in thy name; and we forbad him, because he followeth not with us.