The carbon-nitrogen oxygen (CNO) cycle is one type of fusion reaction by which stars convert hydrogen to helium. The distribution of high energy charges resulting from proton–CNO interaction in space was investigated in the Journal of Physics G: Nuclear and Particle Physics (Nov. 1996). When a high-energy interaction occurs, charged particles are emitted. These particles are classified as shower or heavy particles. The number Y of charged particles that must be observed in order to detect r charged shower particles was shown to follow a negative binomial distribution with P = .75. Use this information to find the probability that five charged particles must be observed in order to detect three charged shower particles.