Monday Tuesday 8 2 6 7 1 Wednesday
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.
Consider the Venn diagram below that represents the number of students that have exams falling on Monday, Tuesday, and Wednesday.
(a) How many students are taking exams on Monday?
(b) How many students have exams on both Tuesday and Wednesday, but not on Monday?
(c) How many students did not have an exam on Monday?
(d) How many students have all their exams on exactly one day (all on Monday, all on Tuesday, or all on Wednesday)?
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