The investigation of the properties of a new solution of TU-cooperative games called a subcore shows that a grand subcore is a multiple selector of the core in a balanced game. Under additional restrictions for the structure of set X⁰(v) optimal solutions of the linear programming problem considered sufficient are obtained for a nucleus to be a selector of a grand subcore. Moreover we proved the proportional nucleus, which is the modification of a nucleus, is a selector of a grand subcore in any balanced n-person TU-game.