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.
i found it very hard to do
i liked the comgination lock problem the best
the first three are easy but the last 2 take some time to figer out
I liked problem 4 because it tells about our combination locks.
i like the combernation one because i like how it was fun
i liked prolem 4 it cool i liked the tree branch tradrgy
I learnt it well the bus captain one was good where you had to put 11 out a hat and you had to pick 3 people. We had to multiply the number of clothing and the answer was 2 x 4 x 3 = 24. And the people that ate chicken and fish 30 + 5 + 10 + 5 = 50.
i liked the combintion one because it was fun adding the numbers
I liked problem 4 the combination locks one
I liked problem six because it is trial and error
I Liked working with the Venn Diagram, it was fun and challenging.
Which fraction of the people at the party onley ate fish?
65%
which fraction of the people at the party onley ate chicken?
60%
which fraction ate the party ate fish and chicken?
35%
which fraction of the party did not eact chicken?
20%
i think these are the answers 🙂
i liked Q5 the best because it was fun