At time \(t=0\) there are an infinite number of molecules of type \(a\) and \(2 n\) molecules of type \(b\) in a two-component gas mixture. After an exponential random time with parameter \(\mu\) any molecule of type \(b\) combines, independently of the others, with a molecule of type \(a\) to form a molecule \(a b\).

(1) What is the probability that at time \(t\) there are still \(j\) free molecules of type \(b\) in the container?

(2) What is the mean time till there are only \(n\) free molecules of type \(b\) left in the container?