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### Unit 8: Lesson 5

Lesson 8: Keeping track of all possible outcomes

# Counting outcomes: flower pots

Find the number of ways you can put four types of flowers into three types of pots.

## Want to join the conversation?

• Is there an easier way to do this instead of having to write out the combonations every time?
• You can just multiply them
• At the beginning of the video would it have been easier to multiply at the beginning?
• Yes, you could have, but Sal has to explain it as well in the video and show how it is a "mathematically legal," or correct, way to solve a problem. Also, he can't just say,"multiply 4*3 to get 12." That would result in an incredibly brief and short video. And there's no point in earning 850 energy points for watching a 4-second video.
; )
• Can't you just make a tree diagram?
• Yes. This method is an alternative, but there are special situations where this method will be required and the same goes for using a tree diagram.
• Why does the counting principle work in telling how many different outcomes there could be for a specific situation in essence, and who came up with this principle?
• The counting principle works by multiplying the number of options of one thing (pots) by the number of options for another (flowers). This basic form of counting works for practically any situation. It is just as simple using larger number as long as you remember: (Total options for A) (Total options for B)= (Number of ways to do A and B together). This basic principle has been around since the earliest days of math (the Romans were known to use pebbles to help with these problems) and there isn't a person on record who claims to have invented it. Once you get into the more advanced counting theorems, you do start to see some big math names, such as Carl Friedrich Gauss and Blaise Pascal, but they created individual theorems, not entire principles.
• So is this sort of like sample space?
• why don't they just make it a multiplication problem. why not just 3x4.
• Sal has to explain why this probability problem equals 12. If he just had a 4 second video that said "3x4=12" then many students would be confused and wonder how he got that answer.
(1 vote)
• could you just multiply 3 x 4 in stead of writing the combinations
• Yes, you can. If you can have 3 types of pots, and 4 types of flowers, just multiply.
• At Sal shows how to find the number of combinations in-between flowers and pots. What about Multiple combinations, for example, to throw in 5 different designs you can add to the pots? How do you do that?
Or what about six-digit combinations to safes? How can you compute the number of possible combinations?
• Thanks to the Counting Principle, you can find the total combinations by multiplying the number of choices for each slot.

For a six-digit combination safe, where each digit is chosen from the digits 0 to 9, you'll find ₁₀C₁ = 10 choices (ways to pick from ten things one at a time) for each of six slots.
``10∙10∙10∙10∙10∙10 = 10⁶ = 1,000,000 = 1 million total combinations for a 6-digit safe``
• Why does he not just tell you the faster way, isn't that the idea of the video? To show you how to figure out these problems the easiest way possible?
(1 vote)
• No. the point of learning is to understand how to think about and solve these types of problems. Sometimes, this means considering several different approaches, not necessarily just the "fastest".
• Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent.

Continent Number of cities
Europe 10
Asia 8
Africa 4
Australia 3

How many different combinations of cities does Elyse have to choose from?

Is there any other way to solve this problem without multiplying?
(1 vote)
• I believe multiplying is the easiest/fastest option but, maybe a chart could work?