To estimate the number of persons interested in recycling aluminum cans, glasses and newspapers. A company conducts a survey of 1000 people and finds that 200 recycles glass, 50 recycles cans and glass, 10 recycle all 3, 300 recycle paper and glass, 450 recycle cans, 60 recycle cans and paper a)how many people do not recycle at all? B)how many people recycle cans only, glasses only and papers only?

In a Venn diagram you draw 3 circles overlapping each other. Name them track, basketball and football respectively. First write 6 where all three circles intersect. That is the number of students that play all three. Now 15 students participate in football and basketball which includes the 6 that participate in all three, so we deduct 6 from 15 and right 9 in the space where basketball and football intersect only. Likewise 9 participate in track and football so we deduct 6 from that and write 3 in the space where track and football intersect only. Same goes for Basketball and track, 8 participants so we deduct 6 and write 2 in the space of intersection of basketball and track only. Now Track has a total of 15 students so we deduct 2 that play track and basketball, then deduct 6 that play both, and deduct 3 that play track and football. This leaves with 4 students that just participate in track. Basketball has a total of 25 out of which 6 play all three, 9 play basketball and football, 2 participate in Basketball and Track. Out of the 25 student in football, 6 participate in all three, 9 participate in football and basketball and 2 participate in basketball and track, this leaves us with 7 (25-6-9-3) students who play just football. When we add all the numbers which is 4 (only track), 8(only basketball), 7 (only football), 2 (basketball and track), 9 (football and basketball), 3 (football and track), 6 (all three), we get a total of 39 students. Deducting 39 from 70 will give us the total number of students that don't participate in any i.e. 31 students.

12 students named swimming,10 name hiking, and 11 named traveling. Four named hiking and swimming, 6 named swimming and traveling, and 3 named hiking and traveling. Two students named all three activities. How many students are in class