# Clothing Combinations and Dinner Menus

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.

# Understanding Fractions

Image Source

Many students struggle with the concept of fractions and it can be difficult to teach because students have many different misconceptions. Some problems can be diagnosed using the following tests:

• a comparisons test with two columns of fractions- ask students to circle the largest fraction or put an equals sign for equivalent fractions
• a number line between zero and 2 – ask students to mark specific fractions on the line.
• Ask students to convert between fractions and decimals
• Convert mixed numbers to improper fractions and the reverse

Next week we will be continuing to learn about fractions by making a poster, “Fractions eight different ways”. Each student will be given a card with a common fraction written on it. They then have to find their partner, by looking for the student with an equivalent fraction. Together, these students create a poster that shows their fraction eight ways:

1. As part of a circle, cake, pizza or pie.
2. As an array – part of a group of items.
3. Written in text (one half, two thirds etc)
4. As a decimal
5. As a percentage
6. Marked on a number line
7. Part of a rod or rectangular shape
8. With a numerator and denominator

Then, students are asked to write problems to which their fraction is the answer. So, for example, problems with the answer two-fifths:

• We shared two cakes between five people, so we each got 2/5 of a cake.
• There were 15 flowers in a vase. 6 of them were red and 9 of them were white. 2/5 of the flowers were red.
• It is 50km from my house to Warrnambool. We pass through Woolsthorpe on our way to Warrnambool after driving for 20km.
• Two out of five chocolates had hard centres.
• 40% of students at school barrack for the Socceroos.