A certain college has 86 students each of whom has to study at least two of the three courses offered.64 students are studying Meteorology,51philosophy,and 62 sociology.
a)how many students study all the three subject?
b)how many are studying Meteorology and Philosophy only?
c)how many are studying Sociology and Philosophy only?
You need to draw a Venn diagram and label each part with a pronumeral. Then you need to express the given information in terms of those pronumerals. Note that there are zero strudents in the parts of the Venn diagram where there is no overlap (because "each of whom has to study at least two of the three courses").
The equations I get (and I'll let you work it out where the symbols were in the Venn diagram I drew) are:
a + b + x = 64 .... (1)
a + c + x = 51 .... (2)
b + c + x = 62 .... (3)
a + b + c + x = 86 .... (4)
Solve these four equations simultaneously for a, b, c and x.
Big hint: x = 5.