200 students

200 students sat exams in Czech, mathematics and physics. 114 students passed Czech, 50 students passed mathematics and 41 students passed physics. 14 students passed both Czech and mathematics, 15 students passed both mathematics and physics, and 11 students passed both Czech and physics. 5 students passed all three exams. How many students did not pass a single exam?

Final Answer:

x =  45

Step-by-step explanation:

n=200  m=5015145=16 f=4115511=10 c=11414511=84  z=m+f+c+14+5+11+15=16+10+84+14+5+11+15=155  x=nz=200155=45



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