7. Three particles \(A , B\) and \(C\) lie at rest in a straight line on a smooth horizontal surface, with \(B\) between \(A\) and \(C\). The particles \(A\), \(B\) and \(C\) have mass \(6 m\), 4 \(m\) and \(m\) respectively. Particle \(A\) is projected towards \(B\) with speed \(3 u\) and \(A\) collides directly with \(B\). Immediately after this collision, the speed of \(B\) is \(w\). The coefficient of restitution between \(A\) and \(B\) is \(\frac { 1 } { 6 }\).

1. Show that \(w = \frac { 21 } { 10 } u\).
2. Express the total kinetic energy of \(A\) and \(B\) lost in the collision as a fraction of the total kinetic energy of \(A\) and \(B\) immediately before the collision. After being struck by \(A\), the particle \(B\) collides directly with \(C\). The coefficient of restitution between \(B\) and \(C\) is \(e\). After the collision between \(B\) and \(C\), there are no further collisions between the particles.
3. Find the range of possible values of \(e\).