A classroom has 20 seats and 18 students. (a) How many different ways are there to select any 2 seats from the 20 available? (b) How many ways are there for the 18 students to occupy the 18 seats that remain after 2 are selected and set aside? (c) How many total ways are there for the 20 students to occupy the 18 seats?
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.
A classroom has 20 seats and 18 students. (a) How many different ways are there to select any 2
seats from the 20 available? (b) How many ways are there for the 18 students to occupy the 18
seats that remain after 2 are selected and set aside? (c) How many total ways are there for the 20
students to occupy the 18 seats?
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