Who had already chosen the eleven disciples before they believed?
God the Father had already chosen and given the eleven disciples to Christ before they believed. Jesus states in John 17 that they were the Father's and were given to Him out of the world. Their coming to faith followed God's prior selection, not the other way around.
Les explains that John 17 is Christ's high priestly prayer, and while Jesus specifically refers to the eleven, they picture all who would one day become the Lord's by salvation. In verse 6 Jesus prays to the Father, 'I have manifested thy name unto the men which thou gavest me out of the world. Thine they were, and thou gavest them to me.' Les emphasizes that those eleven were not believers until Christ came on the scene, so the One who already had His finger on them was God. Then in verse 12 Jesus says He kept them in the Father's name, and none of them was lost.
I have manifested thy name unto the men which thou gavest me out of the world: thine they were, and thou gavest them me; and they have kept thy word.