Combinations are a way to calculate the number of ways to choose a subset of items from a larger set, without considering the order of selection. In other words, combinations are used to count the number of ways to select a certain number of items from a larger group, where the order of selection does not matter.
The formula to calculate the number of combinations of n items taken r at a time is given by:
\[C(n, r) = \frac{n!}{r!(n-r)!}\]
Where:
For example, if you have 5 different colors of pens and you want to choose 2 of them, you can calculate the number of different pairs of pens you can choose using the combination formula:
\[C(5, 2) = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10\]
So, there are 10 different combinations of 2 pens that can be chosen from 5 different colors.
Some important properties of combinations include:
When studying combinations, it's important to understand the concept of choosing items without considering the order of selection. You should also be familiar with the combination formula and how to apply it to different scenarios. Additionally, practice solving problems involving combinations to reinforce your understanding of the topic.
Here are some key points to focus on while studying combinations:
By grasping these concepts and practicing problems related to combinations, you will be well-prepared to tackle any questions or exercises on this topic.
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