At time \(t=0\) a cable consists of 5 identical, intact wires. The cable is subject to a constant load of \(100 \mathrm{kp}\) such that in the beginning each wire bears a load of \(20 \mathrm{kp}\). Given a load of \(w k p\) per wire, the time to breakage of a wire (its lifetime) is exponential with mean value

\[\frac{1000}{w}[\text { weeks }]\]
When one or more wires are broken, the load of \(100 \mathrm{kp}\) is uniformly distributed over the remaining intact ones. For any fixed number of wires, their lifetimes are assumed to be independent and identically distributed.
(1) What is the probability that all wires are broken at time \(t=50\) [weeks] ?
(2) What is the mean time until the cable breaks completely?