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