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Chapter 10: Problem 78

What is a combination?

Short Answer

Expert verified
A combination is a selection of items from a larger set where the order of selection does not matter. It is mathematically represented as \( \binom{n}{k} \) and calculated as \( \frac{n!}{k!(n-k)!} \)

Step by step solution

01

Explanation of Combination

A combination is basically a method of selecting items from a larger set. Unlike permutations, the order of items doesn鈥檛 matter in combinations. For example, if you are selecting 3 books to carry out of 10, the order you carry them doesn't make them any different.
02

Mathematical Definition

In mathematical terms, it is the number of ways to choose k items from n items, also known as a binomial coefficient. It is represented mathematically as \( \binom{n}{k} \) and calculated as \( \frac{n!}{k!(n-k)!} \) where '!' represents factorial.
03

Real Life Examples of Combination

Examples of combinations in real life scenarios might include choosing different toppings for your pizza or selecting a team from a larger group of people. In both these cases, the order of toppings or people doesn鈥檛 matter. What matters is which toppings or people were chosen for the group.

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