A carburetor for the combustion engine in a handheld work apparatus has a carburetor housing in which a carburetor drum is mounted rotatably about a pivot axis. The carburetor drum has a drum body which has at least one channel which runs transversely with respect to the pivot axis and forms an intake channel portion. A sensing unit for sensing at least one rotational position of the carburetor drum is provided. The sensing unit includes a control contour and a sensing device interacting with the control contour. The control contour is formed on the carburetor drum. A method for operating a combustion engine makes provision for the control device to control the supplied quantity of fuel depending on the rotational position, sensed by the sensing unit, of the carburetor drum.