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Introduction to Combinatorics
Combinatorics is a branch of mathematics that deals with counting, arranging and listing of objects. It is used to solve problems related to probability, logic, and decision making.
What is Combinations?
Combinations are a way of selecting items from a set of items without regard to the order in which they are selected. For example, if you have three items (A, B, and C), there are three possible combinations: A and B, A and C, and B and C.
What is Permutations?
Permutations are a way of selecting items from a set of items with regard to the order in which they are selected. For example, if you have three items (A, B, and C), there are six possible permutations: A and B, A and C, B and A, B and C, C and A, and C and B.
What is Factorials?
Factorials are a way of expressing the number of possible permutations of a set of items. The factorial of a number is the product of all positive integers less than or equal to that number. For example, the factorial of 3 is 3 x 2 x 1 = 6.
What is Combinations with Repetition?
Combinations with repetition are a way of selecting items from a set of items with regard to the order in which they are selected and allowing for the same item to be selected multiple times. For example, if you have three items (A, B, and C), there are nine possible combinations with repetition: A and A, A and B, A and C, B and B, B and C, C and C, A and B and A, A and B and C, and B and C and C.
What is a Combination Lock?
A combination lock is a type of lock that uses a combination of numbers or symbols to open the lock. The combination is usually set by the user when the lock is first purchased.
Practice Problems
How many different combinations are there of selecting two items from a set of four items?
How many different permutations are there of selecting two items from a set of four items?
What is the factorial of 4?
How many different combinations with repetition are there of selecting two items from a set of three items?
Suppose you have a combination lock with four numbers. How many different combinations are possible?