Combination and Fundamental Counting Principle

Combination and Fundamental Counting Principle

Combination Word Problems - 1 type of Item

“n”- represents the TOTAL number of items in the group

“r”- represents the number of items being chosen at a time

“ ! ”- exclamation point indicates a factorial, which simply says that you must multiply the number given with the numbers that follow behind in it up to 1

*can be solved by pluggin in values to formula or by calculator

How do Combination Word Problems - 1 type of Item look like?

-Ask you self what is the ONE specific type of item the problem is talking about

How do Combination Word Problems - 1 type of Item look like?

-Ask you self what is the ONE specific type of item the problem is talking about

How are Combination Word Problems 1- type of item Solved?

Calculator Steps:

1) Start input of "n " value

2) PRB -> underline nCr-> Enter

3) End input of "r" value

Combination Word Problems- More than 1 type of Item aka Fundamental Counting Principle

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  1)    Identify how many of 1st type of item

  2)    Identify how many of 2nd type of item

  3)    Identify how many of 3rd type of item

  4)    …etc. if there are more identify how many of each type

  5)    Solve with Fundamental Counting Principle - multiplying

How do Combination Word Problems - MORE that 1 type of Item look like?

-Ask you self what is the MANY DIFFERENT specific type of items the problems is talking about

How do Combination Word Problems - MORE that 1 type of Item look like?

-Ask you self what is the MANY DIFFERENT specific type of items the problems is talking about

How are Combination Word Problems - MORE than 1 type of Item Solved?

Fundamental Counting Principle - Process used to fine the number of ways that a combinations of events can occur

Lets Identify the Type of Combination Word Problem

The following questions will either be 1 type of combination word problems or more than 1 type aka fundamental counting principle

Remember 1 type Combination word problems only mention 1 type of group.

Remember MORE than 1 type aka counting principle mention more than 1 type of item and how many of each kind.

Multiple Choice

Shanna is going to plant a small flower bed. She wants to plant daisies, sunflowers, roses, and fuchsias. What combination of 2 flowers are possible?

• 1 type of combination word problems

• more than 1 type aka fundamental counting principle

Multiple Choice

A men’s department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants. How many different suits consisting of a jacket, shirt, tie, and pants are possible?

• 1 type of combination word problem

• more than 1 type aka fundamental counting principle

Multiple Choice

A chef will make a soup with five ingrediants. One with four meats, one of 4 vegtables, one of 6 broths one of 3 noodles and one of 8 spices.

• 1 type of combination word problem

• more than 1 type aka fundamental counting principle

Multiple Choice

Jessica wants to take three books on vacation with her.She has 5 books to choose from. How many possible combinations of 3 books can she take?

• 1 type of combination word problem

• more than 1 type aka fundamental counting principle

Multiple Choice

Grant is cooking a homemade pizza and he has the following toppings avaible: ham, anchovies, mushrooms and sausage. He will choose 3 of those toppings. How many ways can Grant combine those toppings?

• 1 type of combination word problem

• more than 1 type aka fundamental counting principle

Multiple Choice

Grant is cooking a homemade pizza and he has the following toppings avaible: 4 different types of ham, 2 different types of anchovies, 6 different types of mushrooms and 5 different types of sausage. How many different pizza can he make?

• 1 type of combination word problem

• more than 1 type aka fundamental counting principle

Let's now identify the process we will use to solve for these problems

The following questions will either be 1 type of combination word problems or more than 1 type aka fundamental counting principle

Remember 1 type Combination word problems only mention 1 type of group.

Remember MORE than 1 type aka counting principle mention more than 1 type of item and how many of each kind.

Multiple Choice

Grant is cooking a homemade pizza and he has the following toppings avaible: ham, anchovies, mushrooms and sausage. He will choose 3 of those toppings. How many ways can Grant combine those toppings?

Multiple Choice

Shanna is going to plant a small flower bed. She wants to plant daisies, sunflowers, roses, and fuchsias. What combination of 2 flowers are possible? Which process would you solve this question with?

Multiple Choice

Grant is cooking a homemade pizza and he has the following toppings avaible: 4 different types of ham, 2 different types of anchovies, 6 different types of mushrooms and 5 different types of sausage. How many different pizzas can he make?

Practice Solving

Multiple Choice

A chef will make a soup with five ingredients. One with four meats, one of four vegetables, one of six broths one of three noodles and one of eight spices. Which process would you solve this question with?

• 576

• 25

• 2304

• 1200

Multiple Choice

Grant is cooking a homemade pizza and he has the following toppings avaible: ham, anchovies, mushrooms and sausage. He will choose 3 of those toppings. How many ways can Grant combine those toppings?

• 8

• 12

• 7

• 4

Multiple Choice

Jessica wants to take three books on vacation with her.She has 5 books to choose from. How many possible combinations of 3 books can she take?

• 8

• 10

• 15

• 0

Multiple Choice

A men’s department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants. How many different suits consisting of a jacket, shirt, tie, and pants are possible?

• 192

• 21

• 576

• 786