Solving four operations combination problem using type2 tree structure

Combination problems play an important role in probability theory. The probability of an event is calculated as the ratio of all possible sub-clusters and sub-clusters that provide the desired conditions. It is always difficult to calculate the desired conditions mathematically. Today, developing computer technology is used to overcome this difficulty. The problem of the four operation combinations is often confronted as a competition program played on television programs. It is tried to reach the target number by applying four operations between given numbers in this problem. When performing this operation, operators can be used as many times as required, provided that each number issued is allowed to be used once. In this problem, all possible combinations of four operations include two numbers and a set of operations consisting of one operator. These clusters are based on the intersection of three different clusters. Therefore, a new approach "Type-2 Tree" has been improved for fully model this intersection. In this study, it has been calculated that how many different way the random number is reached for each randomly generated target, as well as determining the rate of reaching the target as the count of given numbers increases. All calculations use programs that written in the Visual Studio 2012 C # environment.