Recently, RIx and the author (7) suggested tha t the dis t r ibut ion over the number of prongs in inelastic hadronie collisions can be explained by assuming I) t ha t the multiplicit ies of pions regardless of thei r charges follow a Poisson dis t r ibut ion and II ) tha t all the possible inelastic final states, which have a given number of part icles and sat isfy the conservation laws of t o t a l isotopic spin, charge and ba ryon number , are equally probable. The predictions of 7:-p inelastic collisions have been given in ref. (1) and agree sat isfactori ly wi th exper iments for P 1 ~ 5 GeV/c. WANG (3), pr ior to our suggestion, proposed a model for mul t ip l ic i ty dis tr ibut ion. He assumed tha t the charged pions in the final states of inelastic hadroulc collisions are produced in pairs in small cells inside the nucleon and tha t the mult ipl ici t ies of these pairs follow a l°oisson distr ibut ion. The neutral pions were also suggested to be produced in the same cellular manner bu t s tat is t ical ly independent of the eharged-pion product ion and these neutrals also follow a Poisson distr ibut ion. The assumption tha t the neutrals and prongs are produced in a s ta t is t ical ly independent manner cannot be exact ly val id because of the isospin constraint . I t is interest ing to invest igate the effect of imposi t ion of isospin constraint on the mult ipl ic i ty distr ibution. Unfor tunate ly , in the case of ~:-p, Wang ' s model cannot predict the dis t r ibut ion for zero prong, and a point to-point comparison of our predict ions wi th his, therefore, is not meaningful. In this connunieation, we will invest igate the mult ipl ic i ty dis tr ibut ion of pp inelastic collisions. Since a zero-prong event is impossible in pp, we ~411 ~chieve a point to-point comparison wi th Wang ' s predictions. Also, the predict ions from Chew and Pignot t i ' s (a) mul t iper iphera l -boots t rap model (hereafter, denoted by CP) will be compared with ours. The calculations will follow closely those in ref. (*). We are going to s t a r t with a Poisson dis tr ibut ion for the number of produced pions m, regardless of the i r charges,