Kaidah Pencacahan 1 - Aturan Penjumlahan dan Aturan Perkalian Matematika Wajib Kelas 12

Assalamualaikum Wr. Wb. Meet me again, Denny Handayani on the Madlife channel. In this video we will learn the subject of the law of decency.

I will share this matter of the law of multiplication in several separate videos and this is the first part of the video. In this first part of the video, we will learn the rules of multiplication and the rules of multiplication. This is a very important matter for friends to master because it will be a prerequisite for the next material when you learn the opportunity. Okay, let's just discuss the material.

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Okay, we will learn the first part of the sub-matter of the first part of the first part of the first sub-matter, namely the rule of multiplication. Well, this is the definition of multiplication rules. If there is K1 how to do the first action, K2 how to do the second action, and so on, and KN how to do the N action, and all the actions are separated.

then there is K1 + K2 + the rest until KN the way to do exactly one of the activities this is the definition later friends will understand more when we start to discuss the example

For the multiplication rule, this is usually used for some incidents that do not happen at the same time or as an option Usually the question is related to the word "atau" but not always For more details, pay attention to the following example Fatih will buy a car in a showroom that provides 3 types of sedan cars, 4 types of SUV cars, and 5 MPP cars

How many choices does Fatih have to buy the car? Okay, here Fatih will only buy one So it's impossible for him to choose everything This is a choice, okay

So how many choices? Here we can use the numbering rule. That is 3 + 4 + 5. So there are 12 choices. Simple, huh? Well, this is the numbering rule. Then the second, there is a multiplication rule.

If there is a K1 way to do the first activity, K2 way to do the second activity, and so on, and there is a KN way to do the N activity, then the whole event can happen with K1 times K2 times the rest until KN way. Well, the characteristic is usually for the rule of thumb, this is for events that happen at the same time, friends. For example,

Tony has 3 clothes and 2 pants How many ways does Tony put on clothes and pants that he owns? Okay, the illustration is like this For example, the 3 clothes that Tony owns are clothes 1, clothes 2, and clothes 3 We will use the tree diagram to put between the clothes he owns and his pants And his pants, he has 2 pants, for example his pants are C1 and C2 Pants 1 and pants 2

This first piece of clothing can be attached to the first skirt. So we get the pair is B1 with C1. The first piece of clothing with the first skirt. Or this first piece of clothing can be attached to the second skirt. Right? So the pair is B1 with C2. The first piece of clothing with the second skirt. The same goes for the second piece of clothing. This second piece of clothing can be attached to the first skirt. Then we get the pair is the second piece of clothing with the first skirt.

And this second shirt can also be paired with the second skirt. Remember, Toni's skirt has two. So it can be paired with B2 and C2, then the pair is B2 and C2. Likewise with the last shirt, the third shirt, can be paired with the first skirt and also with the second skirt.

So we get 2 pairs, B3C1 and B3C2 So many pairs or many ways to install clothes and pants owned by Tony There are as many as 6 ways to install friends Well, if you use a tree diagram like this, it's a bit complicated, especially if for example the clothes that are owned are quite a lot For example, there are 15 clothes, then the pants are 20 for example If we use a tree diagram, it will be very much

For a problem like this, we can immediately use the rule of percalian. So we can just multiply it. Because the clothes and the pants are used together. It is used at the same time. Clearly this is the rule of percalian. We use the percalian rule.

There are many ways to use clothes, right? 3. Many ways to use pants or many choices, there are 2. So many ways to install clothes and pants that Tony owns by using the rule per time is 3 times 2 = 6 ways.

Okay, so that you guys understand more about the difference when we use the multiplication rule and when we use the multiplication rule, now I will discuss some examples of questions, some problems, and we will solve them by using the multiplication rule and the multiplication rule. We start from the first problem, example 1.

Fathia has 4 cars, 3 motorbikes, and 2 bicycles.

How many ways does Fathia go to the office with the vehicle she owns? Guys, pay attention to this event. Maybe Fathia uses the vehicle she owns at the same time. She goes to the office by car, motorcycle, and bicycle. Impossible, right? So this is an option, guys. So this is an option, we have to choose one of them. So this is clear, we use the multiplication rule here.

We just sum it up, there are many ways that Fathia chooses or many ways that Fathia goes to the office with a vehicle that he owns is 4 + 3 + 2 4 this is a lot of cars 3 this is a lot of ways he chooses his motorcycle and 2 this is a lot of ways he chooses his bike So there are 9 ways in total Let's try the second example

Budi wants to listen to songs consisting of 6 dangdut songs, 10 pop songs, and 5 rock songs. How many ways does Budi choose songs to listen to? This is an event that is a choice, friends. Because it is impossible for Budi to listen to 2 songs or more at once.

Try to imagine if we listen to a song together, it's not good, right? So this must be a choice. So Budi will definitely choose one of these choices. So it's clear, this also uses the multiplication rule. Many pop songs have 10, rock 5 and dangdut 6 songs. So we multiply 6 + 10 + 5 = 21 ways. Easy right? Let's continue. Third example.

Hendra has 5 chairs, 6 chairs and 3 shoes. How many ways does Hendra install the clothes he owns? This is similar to the example earlier. Here we use the rules of each time because the chairs, chairs and clothes are used by Hendra together or installed.

Okay, so we use your own rules, the majority of the table is 5, the majority of the pants is 6, and the majority of the shoes is 3, so 5 x 6 x 3 = 90 ways

Okay, easy, huh? Let's continue to the fourth example. From city A to city C must pass through city B. City A to city B is connected by three different routes. And city B to city C is connected by four different routes. How many ways can Budi go from city A to city C? Okay, to make this clearer, we make the illustration.

There are three cities, City A, City B, and City C. City A to City B is connected by three different routes. Okay, for example, this is the first route, this is the second route, and this is the third route. Then, City B to City C is connected by four different routes. From B to C there are four different routes. Let's just say this is the fourth route. It was already three, this is the fourth route, this is the fifth route, this is the sixth route, and this is the seventh route.

Well, if someone wants to go to city C from city A to city C through B, the choice can be like this. You can continue route 1 to 4, you can continue route 1 to 5,

route 1 continues to route 6 or it can also be route 1 continues to route 7 or it can also be from A to B using route 2 2 continues to 4 2 continues to 5 2 continues to 6 2 continues to 7 or from route 3 it can also be 3 4 3 to 5 3 6 or 3 7 now the illustration is like this so we are the same

Like putting clothes between pants So here we use the rules of the times Although the events are not used together, it is impossible that the first and fourth lines are used together But this is related to each other, friends So here we use the rules of the times So many ways Budi goes to city C from city A is 3 times 4 = 12 ways

Okay, now we continue to the fifth example. A plane can choose a flight route from Singapore to Jakarta through three routes. Jakarta-Bali 4 routes, Singapore-Bali 2 routes. Many flight routes can be chosen from Singapore to Bali through Jakarta or directly is

Well, we also made the image like the one before From Singapore then to Jakarta or from Singapore directly to Bali We see from Singapore to Jakarta first Singapore to Jakarta through 3 routes So from Singapore to Jakarta there are 3 routes, friends Then

Jakarta Bali has four routes Jakarta Bali has four routes from Jakarta to Bali there are four 123 and four then from Singapore directly to Bali yes without passing through Jakarta

There are two routes, Singapore directly to Bali, the first route and this is the second route. Now, how many flight routes can be selected from Singapore to Bali, either through Jakarta or directly? So for this case, in the big picture, there are two possible options, friends. The first from Singapore to Bali through Jakarta, or the second from Singapore to Bali directly.

Okay, this is the choice, later we will use the numbering here. Now for the first choice from Singapore to Bali through Jakarta. You see, from Singapore to Jakarta there are 3, then from Jakarta to Bali there are 4. Here we use the rule of multiplication.

3 times 4 equals 12 ways, like the previous question. Then the second choice, directly, without passing through Jakarta. Here there are two ways or two different routes. Same as two ways. Now, because this is a choice, we will sum it up. So 12 + 2 = 14 ways.

Okay, those are 5 examples of questions related to the matter of the multiplication and multiplication rules. Well, to measure how far your understanding is, please try this self-training question. Here I use the national exam question of 2018.

Kota K and Kota L are connected by several routes as shown in the picture below. The question is, if someone leaves from Kota K to Kota L, many alternative routes that can be chosen are? Okay, please try and the answer is written in the comments column. Okay, that's it for our video this time. See you in the next material. Assalamualaikum Wr Wb.