The ruling on combining different types of الطواف depends on which types are being combined. The most common scenario is combining الطواف al-Ifadah (the واجب الحج الطواف performed after عرفة and مزدلفة) with الطواف al-Wada (the farewell الطواف performed when leaving مكة). الشيخ ابن باز ruled that if a الحاج delays الطواف al-Ifadah until the time of their departure from مكة and makes it their last act in the city, this single الطواف suffices for both الطواف al-Ifadah and الطواف al-Wada. The key condition is that no additional activities requiring prolonged stay in مكة should occur after this الطواف.
الشيخ ابن عثيمين confirmed this ruling and explained the principle behind it: the higher-ranking act of worship (الطواف al-Ifadah, which is a pillar/ركن of الحج) encompasses the lesser act (الطواف al-Wada, which is واجب). This is similar to how one who enters the مسجد and performs the واجب الصلاة has also fulfilled the greeting الصلاة (tahiyyat al-masjid) by the stronger opinion.
Regarding الطواف al-Qudum and الطواف al-Ifadah, scholars generally hold that if a الحاج arrives in مكة after عرفة and performs الطواف al-Ifadah, it also covers الطواف al-Qudum, since the time for the arrival الطواف has passed. The اللجنة الدائمة confirmed that these combinations are valid and reduce hardship on الحجاج, especially in the intense الحج schedule.