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My Homework Lesson 6 Use Multiplication To Find Combinations Answers


My Homework Lesson 6 Use Multiplication To Find Combinations Answers




In this article, I will explain how to use multiplication to find combinations and provide some examples and answers from my homework lesson 6. Combinations are ways of selecting items from a set where the order does not matter. For example, if you have a set of three fruits apple, banana, orange, there are three ways to choose one fruit, six ways to choose two fruits, and one way to choose all three fruits. The order of the fruits does not matter, so choosing apple and banana is the same as choosing banana and apple.




My Homework Lesson 6 Use Multiplication To Find Combinations Answers



To find the number of combinations of n items taken r at a time, we can use the formula:


$$\fracn!r!(n-r)!$$


where n! means n factorial, which is the product of all positive integers less than or equal to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120. The formula can also be written as:


$$\binomnr$$


This is read as "n choose r" or "the number of ways to choose r items from a set of n items".


Examples and Answers from My Homework Lesson 6




Here are some examples and answers from my homework lesson 6 using the combination formula. I will also show how to use a tree diagram to find all the possible combinations without repeating any.


Example 1




Amos' team has 3 jersey colors: green, red, and yellow. They can wear orange or black shorts. Find all of the jersey and short combinations for the team.


Answer: To find the number of jersey and short combinations, we can multiply the number of jersey colors by the number of shorts colors. There are 3 jersey colors and 2 shorts colors, so there are 3 x 2 = 6 combinations. They are:



  • green jersey and orange shorts



  • green jersey and black shorts



  • red jersey and orange shorts



  • red jersey and black shorts



  • yellow jersey and orange shorts



  • yellow jersey and black shorts




We can also use a tree diagram to show all the possible combinations. A tree diagram uses "branches" to show all possible outcomes. Here is how it looks:


+-----------------+-----------------+ green jersey red jersey +--------+--------+--------+--------+ v v +--------+--------+ +------+-------+ orange shorts black shorts +--------+--------+ +------+-------+ ^ ^ +-----------------+ v yellow jersey v +-----+-----+ v v +-----+-----+ +---+----+ v v v v orange shorts black shorts


The tree diagram shows that there are six branches, each representing a different combination of jersey and shorts.


Example 2




What are all the possible fruit sorbet combinations if you choose one flavor and one fruit to add in? Complete the tree diagram.


Answer: To find the number of fruit sorbet combinations, we can multiply the number of flavors by the number of fruits. There are 3 flavors (mango, strawberry, vanilla) and 3 fruits (banana, berries, peach), so there are 3 x 3 = 9 combinations. They are:



  • mango sorbet with banana



  • mango sorbet with berries



  • mango sorbet with peach



  • strawberry sorbet with banana



  • strawberry sorbet with berries



  • strawberry sorbet with peach



  • vanilla sorbet with banana



  • vanilla sorbet with berries



  • vanilla sorbet with peach



Here is the completed tree diagram:


+-----------------+-----------------+-----------------+ mango flavor strawberry flavor vanilla flavor +--------+--------+--------+--------+--------+--------+ v v v +--------+--------+ +------+-------+ +------+-------+ banana banana banana +--------+--------+ +------+-------+ +------+-------+ ^ ^ ^ +-----------------+-----------------+ v v +-----+-----+ +-----+-----+ v v v v +-----+-----+ +---+----+ +---+----+ v v v v v v berries peach berries peach


The tree diagram shows that there are nine branches, each representing a different combination of flavor and fruit.


Example 3




A pizza place offers 4 toppings: cheese, pepperoni, mushrooms, and olives. How many different pizzas can you order with exactly 2 toppings?


Answer: To find the number of pizzas with exactly 2 toppings, we can use the combination formula. There are 4 toppings and we want to choose 2 of them, so we have:


$$\frac4!2!(4-2)! = \frac242 \times 2 = \frac244 = 6$$


There are 6 different pizzas with exactly 2 toppings. They are:



  • cheese and pepperoni



  • cheese and mushrooms



  • cheese and olives



  • pepperoni and mushrooms



  • pepperoni and olives



  • mushrooms and olives



We can also use a tree diagram to show all the possible pizzas with exactly 2 toppings. Here is how it looks:


+-----------------+ cheese +--------+--------+ v +--------+--------+ pepperoni +--------+--------+ ^ + + v +-----+-----+ v v +-----+-----+ +---+----+ mushrooms olives


The tree diagram shows that there are six branches, each representing a different pizza with exactly 2 toppings.


Conclusion




In this article, I have explained how to use multiplication to find combinations and provided some examples and answers from my homework lesson 6. I hope this article was helpful and informative. If you have any questions or feedback, please leave a comment below. Thank you for reading!


Sources:



  • [McGraw Hill My Math Grade 3 Chapter 4 Lesson 6 Answer Key Use Multiplication to Find Combinations CCSS Math Answers]



  • [Mathway]



  • [Combination formula (video) Khan Academy]





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