The two last mixed bills of New York City Ballet’s winter season could both be called “New Combinations,” as they both combine world premieres with the less-than-new—for example, Bournonville, from the 19th century. For “New Combinations” proper (January 29 to February 7), Justin Peck tries his hand at Beethoven—the “Eroica” symphony’s first movement—in a dance for six. Beethoven is a particularly daunting assignment for a N.Y.C.B. choreographer, given that the company founder, George Balanchine, felt he shouldn’t be tried. The music, Balanchine said, was so complete—worldmaking, we’d say—that it made choreography redundant. On the other hand, the master appreciated contrariness when driven by conviction and choreographic chops. With “Contemporary Choreography II” (February 5 to 8), fellow resident choreographer Alexei Ratmansky premieres The Naked King, after Hans Christian Andersen’s short story “The Emperor’s New Clothes.” The one-act ballet is a sardonic nod to our own de facto king as well as his sycophantic flunkies. Ratmansky possesses a brilliant knack for the comedy of dumb power. For this outing, he has Jean Françaix’s witty 1935 score for the Paris Opera Ballet to help. —Apollinaire Scherr