What is Handshaking Problem?
Handshaking problem is one of the most interesting problems in mathematics. It is used to find that in a room full of people how many handshakes are required for everybody to shake everybody else’s hand exactly once?
Example: The table given below tells us about the minimum number of handshakes required for various groups of people.
Basically when there are 2 people there will be two handshakes and if there are three people there will be 3 handshakes and so on.
This many people we can count but let’s suppose there are thousands of people in a hall then we can’t count each handshake here the need for the combination arises.
Number of People | Possible Combinations | Minimum Handshake required |
---|---|---|
Two People | A-B | 1 handshake |
Three People | A-B A-C B-C | 3 handshake |
Four People | A-B A-C A-D B-C B-D C-D | 6 handshake |
Combinations
Combination is a way of choosing items from a set, such as (unlike permutations) the order of selection doesn’t matter. In smaller cases, it’s possible to count the number of combinations. Combination refers to the mixture of n things taken k at a time without repetition. To know the combinations in the case where repetition is allowed, terms like k-selection or k-combination along with repetition are often used.
Combinations are particularly useful in scenarios where the outcome depends on the presence or absence of items rather than their sequence, making them a fundamental tool in various probability and statistical analyses, as well as in everyday decision-making processes that involve selecting subsets from a larger set.
In this article, we will learn about combinations in detail, along with their formulas, how to calculate combinations, etc.
Table of Content
- What is Combination in Maths?
- Basic Principles of Counting
- Combination Formula
- Permutations and Combinations
- How to Calculate Probability of Combinations?
- What is Handshaking Problem?
- Handshaking Combination
- Examples on Combinations
- Combinations Class 11
- Practice Problems on Combinations