120 first year science students in a university sat an examination in Mathematics. There were three papers analysis, geometry and calculus. 1 34 students passed all the three papers 52 students passed the geometry and calculus papers 20 students passed in analysis and geometry but failed Calculus 60 students passed only two out of three papers 80 students passed the analysis paper 78 students passed the geometry paper 12 students passed only one paper. (a) How many students failed all the three papers?
​