This paper considers the downlink transmission of an intelligent reflecting surface (IRS)-aided multi-carrier (MC) non-orthogonal multiple access (NOMA) system, referred to as the IRS-aided MC-NOMA system. Due to the limitations on the availability of the IRS, a limited number of channels can be served with the support of the available IRS units. Therefore, a competitive approach is proposed to assign the available IRS units for the intended channels, and to group the users in each channel (i.e., clustering). To validate the effectiveness of the proposed competitive approaches, a power minimization problem is considered that aims to minimize the total transmit power while ensuring a set of quality-of-service requirements. Because of the non-convex nature of the joint power optimization problem, we develop a simple sequential convex approximation algorithm to solve it. Simulation results demonstrate that the IRS-aided MC-NOMA system with proposed IRS-assignment and grouping approaches outperforms the random IRS-assignment and grouping approaches regarding the transmit power consumption.