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Statistics and probability

Course: Statistics and probability>Unit 8

Lesson 1: Counting principle and factorial

Counting outcomes: flower pots

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

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• 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.
• i don't get anything that it is showing and im starting to get mad/stressed and when are we going to use this?
• Well, it might be used for higher studies depending on what profession you choose. For example, weather forecasting, insurance, sports outcomes and even medical diagnosis.
• 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".
• So is this sort of like sample space?
(1 vote)
• why don't they just make it a multiplication problem. why not just 3x4.
(1 vote)
• 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
(1 vote)
• Yes, you can. If you can have 3 types of pots, and 4 types of flowers, just multiply.
``10∙10∙10∙10∙10∙10 = 10⁶ = 1,000,000 = 1 million total combinations for a 6-digit safe``