# Combination Problems

## Using n!/r!(n - r)! to calculate permutations

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Practice Combination Problems

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Combinations
Teacher Contributed

## Chance in Lottery Games

### Topic

Chance in Lottery Games

• Combination
• Permutation
• Probability

### Student Exploration

#### What are your chances of winning the lottery?

The California Fantasy 5 game is a state lottery game played across the state. Anyone eighteen-years-old or older can buy a ticket at a local convenience store. All you have to do is pick five lucky numbers from 1 to 39 on a Fantasy 5 slip. Then every day at 6:30pm entries are closed and the state draws the five Fantasy 5 numbers for the day. Read more about the pickings at http://www.calottery.com/play/draw-games/fantasy-5. Now for the winnings! You win if you get one of the four following outcomes. You pick 2 of the 5 winning numbers, you pick 3 of the 5 winning numbers, you pick 4 of the 5 winning numbers, and you pick 5 of the 5 winning numbers.
What is the probability of picking 5 of the 5 winning numbers?

### Extension Investigation

a. Why does this situation represent a Combination?
b. How many different ways can all five of the Fantasy 5 numbers be picked?
c. How many different ways can four of the five Fantasy 5 numbers be picked?
d. If you were analyzing how many ways that two of the five numbers could be picked, how would you approach solving this problem differently?
e. If you were asked to find the probability of picking four of the five Fantasy 5 numbers correctly, how would you approach that task?
f. What would need to change in the problem in order for it to represent a Permutation?

### Connections to other CK-12 Subject Areas

• Permutations Problems
• Permutations and Combinations Compared
• Theoretical and Experimental Probability

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
The text passage provides background information on the California Fantasy 5 lottery game, including how to play and the different ways to win. It then poses a question about the probability of picking 5 of the 5 winning numbers.
single_question

the passage contains a single mathematical question: "what is the probability of picking 5 of the 5 winning numbers?" however, no answer to this question is provided in the text.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Combination Problems

## Using n!/r!(n - r)! to calculate permutations

Estimated6 minsto complete
%
Progress
Practice Combination Problems

MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated6 minsto complete
%
Combinations
Teacher Contributed

## Chance in Lottery Games

### Topic

Chance in Lottery Games

• Combination
• Permutation
• Probability

### Student Exploration

#### What are your chances of winning the lottery?

The California Fantasy 5 game is a state lottery game played across the state. Anyone eighteen-years-old or older can buy a ticket at a local convenience store. All you have to do is pick five lucky numbers from 1 to 39 on a Fantasy 5 slip. Then every day at 6:30pm entries are closed and the state draws the five Fantasy 5 numbers for the day. Read more about the pickings at http://www.calottery.com/play/draw-games/fantasy-5. Now for the winnings! You win if you get one of the four following outcomes. You pick 2 of the 5 winning numbers, you pick 3 of the 5 winning numbers, you pick 4 of the 5 winning numbers, and you pick 5 of the 5 winning numbers.
What is the probability of picking 5 of the 5 winning numbers?

### Extension Investigation

a. Why does this situation represent a Combination?
b. How many different ways can all five of the Fantasy 5 numbers be picked?
c. How many different ways can four of the five Fantasy 5 numbers be picked?
d. If you were analyzing how many ways that two of the five numbers could be picked, how would you approach solving this problem differently?
e. If you were asked to find the probability of picking four of the five Fantasy 5 numbers correctly, how would you approach that task?
f. What would need to change in the problem in order for it to represent a Permutation?

### Connections to other CK-12 Subject Areas

• Permutations Problems
• Permutations and Combinations Compared
• Theoretical and Experimental Probability

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
user
The text passage provides background information on the California Fantasy 5 lottery game, including how to play and the different ways to win. It then poses a question about the probability of picking 5 of the 5 winning numbers.

TYPE: SINGLE_QUESTION

The passage contains a single mathematical question: "What is the probability of picking 5 of the 5 winning numbers?" However, no answer to this question is provided in the text.