

Combinations, formula, practice & examplesArrangements without Order In math, a combination is an arrangement in which order does not matter. Often contrasted with permutations, which are ordered arrangements, a combination defines how many ways you could choose a group from a larger group.
Note: To understand this topic, it is highly advisable to be familiar with factorial notation .
This Page: combination formula combination practice problems Related pages:advanced combinations  permutations lesson combinations vs permutations  factorials The formula for combinations:To find all of the differennt ways to arrange r items out of n items. Use the combination formula below. (n stands for the total number of items; r stands for how many things you are choosing.)
Practice Problems: combinations
Directions: Apply the combination formula to solve the problems below.
Problem 1) In a class of 10 students, how many ways can a club of 4 students be arranged? Answer Problem 2) Eleven students put their names on slips of paper inside a box. Three names are going to be taken out. How many different ways can the three names be chosen?
Answer Problem 3) Over the weekend, your family is going on vacation, and your mom is letting you bring your favorite video game console as well as five of your games. How many ways can you choose the five games if you have 12 games in all?
Answer _{12}C_{5} = (12)!/(5!×(125)!)=(12)!/(5!×(7)!) (12 ×11×10×9×8×7!) /(5!×7!) = 792 This Page: combination formula combination practice problems Related pages: advanced combinations  permutations lesson combinations vs permutations  factorials 