In a group of 150 students, 52 like tea, 48 like juice and 62 like coffee. If each student in the group likes at least one among tea, juice and coffee, then the maximum number of students that like…

At most 12 students can like more than one drink. The total of $52+48+62=162$ memberships includes 12 extra memberships beyond the 150 needed to give everyone one drink, and every student who likes multiple drinks contributes at least one extra. The bound is attained with 12 tea-and-juice drinkers and single-drink counts of 40 for tea, 36 for juice and 62 for coffee. The count 6 uses two extra memberships for every student who likes multiple drinks, which describes only the students who like all three.