Complete question :
In a class of 125 students, 27 are computer science majors, 51 are mechanical engineering majors, 12 are civil engineers and the rest are general engineering majors. Assume students only have one major.
Suppose six students from the class are chosen at random what is the probability none are mechanical engineering majors?
Answer:
0.039
Explanation:
Total = T = 125
Computer Science = S = 27
Mechanical Engineering = M = 51
Civil Engineering = C = 12
General engineering, G = 125 - (27 + 51 + 12) = 35
Probability that none out of six chosen at random are Mechanical Engineering major :
Probability = required outcome / Total possible outcomes
Non mechanical engineering majors = 125 - 51 = 74
Probability none of 6 selected are mechanical engineering majors :
74C6 / 125C6
Recall :
nCr = n! / (n-r)! r!
, using calculator :
74C6 / 125C6 = 185250786 / 4690625500
= 0.0394938
= 0.039