120 High school students have to do 3 final exams to be able to enter to the university. There are exams in Math, CS and Language. We know: - 60 students passed Math - 40 students passed CS - 30 students passed CS and Math - 30 students passed Language and Math - 25 students passed CS and Language - 20 students passed Language and Math and CS - 50 students – failed all 3 exams. Draw a Venn Diagram to illustrate sets of students passing different exams. How many students passed Language?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
120 High school students have to do 3 final exams to be able to enter to the university. There are exams in Math, CS and Language. We know:
- 60 students passed Math
- 40 students passed CS
- 30 students passed CS and Math
- 30 students passed Language and Math
- 25 students passed CS and Language
- 20 students passed Language and Math and CS
- 50 students – failed all 3 exams.
- Draw a Venn Diagram to illustrate sets of students passing different exams.
- How many students passed Language?
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