A market research group conducted a survey of 2000 consumers and reported that 1720 consumers liked product `P_1` and 1450 consumers like product `P_2dot` What is the least number that must have liked both the products?

In a survey, 50 people like product A, 30 people like product B and 20 people like product C and 35 people like exactly two products. If 5 people like all the three products then number of people who do not like any product . [There are 100 people in survey]