The ruling on combining different types of tawaf depends on which types are being combined. The most common scenario is combining Tawaf al-Ifadah (the wajib Haji tawaf performed after Arafah and Muzdalifah) with Tawaf al-Wada (the farewell tawaf performed when leaving Mekkah). Sheikh Ibn Baz ruled that if a jamaah haji delays Tawaf al-Ifadah until the time of their departure from Mekkah and makes it their last act in the city, this single tawaf suffices for both Tawaf al-Ifadah and Tawaf al-Wada. The key condition is that no additional activities requiring prolonged stay in Mekkah should occur after this tawaf.
Sheikh Ibn Uthaymeen confirmed this ruling and explained the principle behind it: the higher-ranking act of worship (Tawaf al-Ifadah, which is a pillar/rukun of Haji) encompasses the lesser act (Tawaf al-Wada, which is wajib). This is similar to how one who enters the masjid and performs the wajib shalat has also fulfilled the greeting shalat (tahiyyat al-masjid) by the stronger opinion.
Regarding Tawaf al-Qudum and Tawaf al-Ifadah, scholars generally hold that if a jamaah haji arrives in Mekkah after Arafah and performs Tawaf al-Ifadah, it also covers Tawaf al-Qudum, since the time for the arrival tawaf has passed. The Permanent Committee confirmed that these combinations are valid and reduce hardship on jamaah haji, especially in the intense Haji schedule.