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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.

## Want to join the conversation?

• Is there an easier way to do this instead of having to write out the combonations every time?
(36 votes)
• You can just multiply them
(73 votes)
• At the beginning of the video would it have been easier to multiply at the beginning?
(9 votes)
• 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.
; )
(50 votes)
• Can't you just make a tree diagram?
(8 votes)
• 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.
(6 votes)
• 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?
(2 votes)
• 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.
(9 votes)
• i don't get anything that it is showing and im starting to get mad/stressed and when are we going to use this?
(2 votes)
• 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.
(2 votes)
• 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".
(4 votes)
• 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.
(3 votes)
• 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?
Please respond, because I have exams and really need these answers!
(1 vote)
• 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``
(2 votes)

## Video transcript

- [Voiceover] You're at a florist store and you're interested in buying some type of a potted flower. And you ask the florist, "What type of flowers do you sell?" And he says, "Well we sell four types of flowers, we sell "roses, tulips, sunflowers, and lilies." And you say, "What type of pots could I put them in?" And he says, "Well you could pick any flower, and then you "could pick any of our three pots, we have brown pots, "we have yellow pots, and we have green pots." So, the question that I ask to you is, how many types of, I guess, flower and pots put together can you walk out of this florist store with? For example, you could get a rose and a brown pot, you could get a rose and a green pot. Or you could get a yellow pot that has a sunflower in it. Or a yellow pot that has a lily in it. So, how many scenarios could you walk out of that store with? And like always, I'll encourage you to pause the video and try to figure it out on your own. Let's think through it. I'll just write the first letters, just to visualize or just so I don't have to write down everything. So, you could have a brown pot, you could have a yellow pot, or you could have a green pot. You difinitely have to pick a pot, so you're going to have one of those. And then for each of these three, there's four possible flowers you could have. You could have a rose with the brown pot, you could have a rose with the yellow pot, you could have a rose with the green pot. You could have a tulip with the brown pot, a tulip with the yellow pot, a tulip with the green pot. You could have a sunflower with each of the three pots, or you could have a lily with the brown pot, a lily with the yellow pot, and a lily with a green pot. So, how many scenarios are we talking about? Well, we had three pots, so we have three pots right over here, and we have four possible flowers to put in the pots, and so we see that we have four possible flowers for each of the three pots. It's going to be three times four possibilites, or 12. You see them right over here. This is brown with rose, brown with tulip, brown with sunflower, brown with lily. Yellow with rose, yellow with tulip, yellow with sunflower, yellow with lily. So, if we count these, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve. Twelve possible pot, flower scenarios to walk out of that florist store with.