In a system of particles,internal forces can change (for the system)

Why do internal forces acting within a system not affect its motion?

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When both the persons jump simultaneously with the same speed,then:

Why are the internal forces acting on the centre of mass of a system neglected?

The multiplication of the total mass of a system and the acceleration of its centre of mass denotes what?

Choose the correct statement$(s)$:
$(A)$ The position of the centre of mass of a system is dependent on the choice of coordinate system.
$(B)$ Newton's second law of motion is applicable to the centre of mass of the system.
$(C)$ Internal forces cannot change the state of the centre of mass.
$(D)$ Internal forces can change the state of the centre of mass.