Problem 1: Imagine you had three different pairs of pants in your wardrobe and four different tops. How many different combinations could you wear? How can you work it out for any number of articles of clothing? Now add two hats. How many outfits could you put together? To make the most out of your wardrobe (that is, most combinations) would you add another pair of pants, top or hat?
Problem 2: Three bus captains are to be chosen by putting 11 names in a hat – How many different combinations are possible?
Problem 3: At a buffet dinner, you have a choice of two soups (pumpkin or spring vegetable), four different main courses (chicken, lamb, beef or vegetarian) and three desserts (fruit salad, chocolate mousse or cheesecake). How many different combinations of three course meals could there be?
Problem 4: Your “combination” lock on your locker (really should be called a “permutation” lock, because the order of the numbers does matter!) has three numbers, each from zero to 39. What is the total number of possible lock combinations?
Problem 5: In a group of school students, 26 people barrack for Geelong and 32 like playing cricket. How many people might there be in the group? (You may like to use a Venn diagram or a table to help with this question. – Thanks to Peter Sullivan for this question).
Problem 6: At a party there were 50 people; 35 ate some of the fish, 30 ate some of the chicken dish and 5 ate nothing. Draw a diagram to show this information. Work out:
- what fraction of the people at the party ate only fish?
- what fraction of the people at the party ate only chicken?
- what fraction of the people at the party ate both fish and chicken?
- what fraction of the people at the party did not eat chicken?
More about Combinations and Permutations from Dr. Maths at the Maths Forum.
And even more about Combinations and Permutations from Maths is Fun!
Write a comment below to tell me the answer to the problem you liked best and tell me why you thought that was the most interesting problem.