Consider the set of numbers {1,...,200}. Denote by A the set of multiples of 2 in this set. Denote by B the set of multiples of 5 in this set. Denote by the set of multiples of 11 in this set. How many numbers in {1,...,200} are divisible by at least one of 2,5 and 117 How many numbers in {1,..,200} are relatively prime to 110? (Relatively prime means they do not share any factors.) How many numbers in {1,...,200) are divisible by 2 and 11 but not by 5? How many numbers in {1,...,200) are divisible by 2 or 11 but not by 5?
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 set of numbers {1,...,200}. Denote by A the set of multiples of 2 in this set. Denote by B the set of multiples of 5 in this set. Denote by the set of multiples of 11 in this set. How many numbers in {1,...,200} are divisible by at least one of 2,5 and 117 How many numbers in {1,..,200} are relatively prime to 110? (Relatively prime means they do not share any factors.) How many numbers in {1,...,200) are divisible by 2 and 11 but not by 5? How many numbers in {1,...,200) are divisible by 2 or 11 but not by 5?
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