Practice Problems on Combinations
Q1. A classroom has 20 students, and a committee of 4 students needs to be formed to organize an upcoming event. In how many ways can this committee be chosen?
Q2. You have 5 different books on mathematics and want to select 3 to place on your desk for quick reference. In how many ways can you choose which 3 books to place on the desk?
Q3. A fruit shop offers baskets that can contain any combination of 3 different fruits from their selection of 5 different fruits (apple, banana, cherry, date, and elderberry). How many different fruit baskets can be made?
Q4. A lottery game requires you to choose 6 numbers out of a possible 49. How many different combinations of numbers can you choose?
Q5. From a pool of 12 jurors, a jury of 6 needs to be selected for a trial. In how many different ways can the jury be formed?
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