Combinations

Learning Objectives Define what a combination is in the context of selecting items. Distinguish between situations where order matters (permutations, implicitly) and where it does not (combinations). Systematically list all possible combinations for a small set of items. Identify and avoid duplicate selections when forming combinations. Apply the concept of combinations to solve simple real-world selection problems. Determine the total number of combinations for a given selection problem by listing. Have you ever had to choose a few items from a larger group, like picking toppings for a pizza or friends for a team? 🍕 What if the order you pick them in doesn't change the final group? In this lesson, you'll learn about 'combinations' – a way of selecting...

TermDefinitionExample CombinationA selection of items from a larger group where the order in which the items are chosen does not matter. The group itself is what counts.Choosing 2 fruits (apple, banana) from a basket is a combination. (Banana, apple) is the same combination. SelectionThe act of choosing one or more items from a larger collection or set.If you have 3 shirts and you choose 1 to wear, that's a selection. Order Matters vs. Order Doesn't MatterThis describes whether changing the sequence of selected items creates a different outcome. If order matters, it's not a combination. If order doesn't matter, it is a combination.Order matters for a locker code (1-2-3 is different from 3-2-1). Order doesn't matter for choosing 2 friends for a movie (Sarah then Jo...

The 'Order Doesn't Matter' Rule When selecting a group of items, if rearranging the items within that group does not create a new or different group, then you are dealing with a combination. This is the fundamental rule for identifying a combination problem. Always ask yourself: 'Does the order of selection change the outcome?' If the answer is 'no,' then it's a combination. The Systematic Listing Rule To find all possible combinations for a small number of items, create a list by starting with one item and pairing it with all subsequent items, then moving to the next item and repeating, ensuring you do not repeat groups already formed. This rule helps you organize your thoughts and ensures you find every possible combination without m...