Mathematics
Grade 3
15 min
Combinations
Combinations
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the number of choices in different groups.
Use multiplication to find the total number of possible combinations from two groups.
Solve simple word problems about combinations.
Draw a simple diagram or chart to show all possible combinations.
Explain why multiplication is a faster way to find combinations than listing them all out.
Create their own combination problem with two groups of items.
If you have 3 different shirts and 2 different pairs of pants, how many different outfits can you make? 👕👖 Let's find out!
Today, we will learn a fun and fast way to find out how many different combinations we can make when we have choices from different groups. We will use our multiplication skills to become combination experts! This helps us solve...
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Key Concepts & Vocabulary
TermDefinitionExample
CombinationA combination is one way of putting items together when you choose one item from each group.One red shirt and one pair of blue pants is one combination for an outfit.
GroupA set of similar items you can choose from.A pile of all your shirts is one group. A pile of all your pants is another group.
ChoiceA single item within a group that you can pick.In a group of shirts (red, blue, green), the red shirt is one choice.
PairA combination made of two items, with one item chosen from each of two groups.A scoop of chocolate ice cream with sprinkles is a pair.
Total Possible CombinationsThe final number of all the different ways you can combine items from the groups.If you have 6 different outfits you can make, the total possible combinations is 6.
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Core Formulas
The Multiplication Rule for Combinations
(\text{Number of choices in Group 1}) \times (\text{Number of choices in Group 2}) = (\text{Total Combinations})
To find the total number of combinations, you multiply the number of choices from the first group by the number of choices from the second group.
The 'For Each' Pattern
For each choice in Group 1, you have all the choices from Group 2.
This helps you understand why multiplication works. If you have 3 shirts, you think: 'For the first shirt, I can wear it with 2 different pants. For the second shirt, I can wear it with 2 different pants...' and so on.
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Challenging
You are building a robot. You can choose 1 of 3 heads, 1 of 4 bodies, and 1 of 2 pairs of legs. How many different robot combinations can you build?
A.9
B.12
C.24
D.14
Challenging
A smoothie shop's sign says, 'Choose from our 6 fruits and 5 vegetables to make a combo. We have over 40 different combinations!' Is the sign's claim true?
A.No, because 6 + 5 = 11, which is not over 40.
B.Yes, because 6 x 5 = 30, and you can add 10 to get over 40.
C.No, because 6 x 5 = 30, which is not over 40.
D.Yes, because 6 and 5 are big numbers.
Challenging
To make a design, you must pick one pattern and one color. The total number of possible designs is 24. Which of these could be the number of patterns and colors you have to choose from?
A.12 patterns and 12 colors
B.20 patterns and 4 colors
C.6 patterns and 4 colors
D.2 patterns and 10 colors
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