All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The general rule in Islamic Law is that gambling is forbidden since Allah the Almighty says {what means}: "O ye who believe! Intoxicants and gambling, (dedication of) stones, and (divination by) arrows, are an abomination,- of Satan’s handwork: eschew such (abomination), that ye may prosper." {Al-Ma`idah, 90}. Another reason is that one person wins at the expense of other participants leading to conflict, enmity, and eating up people`s wealth unjustly.
As understood from the above question, participants pay a portion of the car`s value so that one of them wins the car, but this is gambling itself. As for the partnership and ownership amongst the participants, it is just a cover for the real thing, gambling, which involves the sale method. The proof of this is that the participants` ownership is terminated the moment one of them wins the car whose ownership is actually snatched from the participants. ‘Abdallah b. ‘Amr told that the Prophet forbade wine and maisir." {Transmitted by Abu Dawud}. Al-Bajirmi, may Allah have mercy on his soul, commented "His saying maisir" refers to gambling where it is likely to win or lose. It is considered a major sin if it was for money and a minor sin if it wasn`t." {Hasheyat Al-Bajirmi Ala Shareh Al-Menhaj, Vol.4, Page376}.
In conclusion, the project mentioned in the above question is prohibited in Islam because it rests on gambling as well as eating up people`s wealth unjustly. And Allah the Almighty knows best.