Suppose there are two football coaches living there in your hometown, Coach Calvin and Coach Arminian.
Coach Calvin is in a league where he hand picks his players.
Coach Arminian is in a league where individuals volunteer to join the team.
Coach Calvin predetermined who would be on his team, while Coach Arminian allowed his team to join voluntarily. However, one thing they both had in common is that prior to the teams being formed both coaches had predetermined to conform their team members into conditioned football players.
Calvinists insist Roman 8 and Eph. 1 (where predestination is mentioned) must mean that God is like "Coach Calvin" but all the passage tells us is what the coach has predetermined for his team, it says nothing about his predetermining who would and would not be on that team.
Calvinists make arguments such as this: "whom he did predestinate, them [the same ones] he also called: and whom he called, them [the same ones] he also justified: and whom he justified, them [the same ones] he also glorified."
The problem with this is that Paul is only listing the things God has done for those who love him. He is not even bringing up men's response. Even Calvinists insist that a man must respond in faith in order to be justified, but this verse doesn't even mention faith. Should we conclude from this that faith is not necessary? Of course not, no one does. Should we conclude from this that faith must be irresistably applied to those foreknown, predestined and called? Only if you want to infer something from silence. Simply because Paul assumes the faith response doesn't necessarily mean that such a response is not free, or is somehow irresistably applied to certain individuals to the neglect of others. You have to read that into the text. All we can certainly conclude from this passage is that God has predetermined for US, his church, to be conformed to the image of his son and the we, his church, were called, justified, sanctified and glorified.
If we want to learn more about the response of faith we need to look at other passages, not this one.