You are given a $2$ x $3$ board and a robot initially placed at the upper left corner. On each step, the robot can either move one cell to the right $($R$),$ or one cell down $($D$).$ Design a C$++$ program which is able to calculate and show the number of paths the robot can move from the source cell $($the upper left corner$)$ to destination cell $($the lower right corner$).$