An environmental sub-committee comprising 3 members and an infrastructure subcommittee comprising 2 members are to be constituted from a committee of 12 members. In how many ways can these two sub-committees be selected from among the 12 committee members provided no member can be at two sub-committees at the same time?

(b) The proprietor of an office building wants to know the preferred air temperature inside the building by people who work in there. He conducts a survey of 120 randomly selected office workers as to whether they are more comfortable in 240 C or in 200 C. Based on his survey he discovers that 70 workers start work early and leave early, and among those 30 prefer 240 C. Of the remaining workers who start late and work till late, 23 have said their preferred temperature is 200 C. Construct the contingency table and determine the probability that a randomly selected worker starts early given that his or her preferred temperature is 200 C.

(c) The Venn diagram below shows a total of 268 students in science in a high school. Among them A represents 92 students studying physics, B represents 98 students studying chemistry and C represents 110 students studying mathematics. Twelve students are studying both physics and chemistry, 10 students are studying both chemistry and mathematics and 14 students are studying both physics and mathematics. How many students are studying all three subjects?