Wellington held all three Secretary of State positions. ^ He also held office as First Lord of the Treasury.
As no separate Chancellor of the Exchequer had been appointed, Denman held the post pro tempore by virtue of being Lord Chief Justice.
Most offices were in commission.
Wellington caretaker ministry Wikipedia
King William IV had dismissed the Whig government of Lord Melbourne on 14 November 1834 and asked the Duke of Wellington to form a government but he declined, instead recommending Sir Robert Peel. Peel was in Italy at the time, so the Duke of Wellington took control of the government until Peel returned and was able to form his government on 10 December.