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Complete Permutations and Combinations (क्रमचय और संचय) for All Competitive Exams – Transcript
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Summary
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- The fundamental principle of counting or multiplication principle states that when two events are both necessary, the total combinations are found by multiplying the possible cases of each event.
- For distinct objects arranged on R places when repetition is not allowed, the permutation formula is given by n factorial divided by n minus r factorial, represented as NPR.
- In permutations, the order and position of objects matter, whereas in combinations for selecting items, the order does not matter.
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Hello everyone, I hope you all are healthy. Today we are starting Permutation and Combination. We have made a slight change in our syllabus. Now probability will also be asked in SSC Gal Tier 2. And if probability is given, it means that questions can be made from permutation as well. Because we cannot do probability unless we have complete knowledge of permutation and combination, so first I will understand the permutation combination very well. Once this is understood, after that we will start probability, then you should not face
any problem in doing date probability. And Combination All Two was not given separately in the syllabus but its questions can be asked at all times. Many times questions of permutation have been asked in number system also. Okay, so earlier also we had read a little bit about the basic permutation combination in number system also. Here, I will teach you in complete detail so that whatever exam you are giving, UPSC, CDS, Banking exams, any other exam in which permutation combination is asked, you can comfortably answer your questions. As soon as our
fermentation combination and after that probability is done, it means that our maths will be finished for every competitive exam. Okay, after that you do not need to save anything, see, once you have done maths course, you can do it for every exam . If there is any change in the syllabus, it is still okay . We do not need to know what is Permutation and Combination and Sanchay, it is okay in the session, just you are this man. Let's find out
the total number of ways by which we can reduce one, okay, we use permutations and combinations to get that, okay, I will explain it to you with two-three examples from two-three registrations, this should be in your mind. You will sit in such a way that you will never forget and you will enjoy asking its questions. Okay, I am going to study formula free. In today's class, I am not going to teach you even a single formula. I will make you ask all the questions from basic. You will enjoy it. The level of questions is very high. I am also going to go high
, okay, there will be one or two questions like this, it is very difficult, but I am teaching, but the chances of appearing in the exam will be less, okay, then see them, it is your choice, rest of the maximum questions should be important for you, okay with me. What should you search in the house? Now you have to go to a function somewhere. Okay, what is there in your wardrobe? There are two shirts lying there and you have three pants lying there. Okay, so when you wear them and go,
it is not possible that both of you What would you do in general? What would you do in general? We would wear a shirt and under it, what would we do? We would wear a pant. If we do something like this, then I have to choose how many ways I can make my combination with so many triangles. From I can do a paint and extra thing out of this if I talk about that so how do we do this okay if I
name this shirt de dun 6 months this t-shirt van this is the shirt I have you this is the one I have This is a paint van, this is what I have with me, you are a pan, and this is what I have with me, I have two shirts, three paints, if I start making combinations, how will I become, you are this person, like you have to choose, I said, this is what I have with me, this is a shirt, van. And this is what I have, okay, it may be that I choose the shirt van and it
may also be that I will give it to you, if I choose the shirt van then what do I have over the pant, you will say sir, what will I have to do shirt? Is this thing possible with Van? Like this, if I do the shirt thing, then with this I have all three things possible that I can wear pan, van, paint and
anything else with the shirt. If I look at the total, first case. What happened to me, here I took shirt only pant, here I took shirt, only pant, here I took shirt, only pant, here I took shirt, van here, here I took shirt, only pant, here I took shirt, I will become the first shirt. Also, if I can wear all three types of pants, then
I have three combinations, and if I talk about it, I can take another shirt, then I have three combinations, so total 3 + 3, so many combinations, six. I can dress up in six ways in one function. Can I go, did I understand this thing? I did the basic process. I will tell you the direct way of what is happening. Did I understand this thing? I said, I had two types of shirts, I had three types of pants, so what should I do? What could I have done? First I put a shirt, I
can wear all three pants with it, then I put another shirt, all three pants with it, one each with this shirt. If I get all three pants, then three combinations will be formed. If I get all three pants with this shirt, then three combinations will be made. Three plus three. How many combinations do I have? I can get ready in six ways. So many parts are clear to go to the function. I can even see it upside down. You could have said, Sir, what do I have, there are three types of pants, this shirt is van, this shirt is tu, so I choose pant van first,
which shirt is made with pant van, shirt is fine, shirt is tu too, so two combinations. And with Pant 3, both of you [ __ ] can be done, so again I have two combinations, 2 plus 2 two, in how many ways or six combinations are being formed with me, and is this thing fixed here that you have to Pant? Are you wearing a shirt too? Is it possible that you are going to a function wearing an empty shirt and without wearing pants? Or can you wear empty pants and roam around shirtless?
You have to wear both things if you want to look like this. So, you will wear a shirt and you will also wear a pant, so what do I have with both the things that are necessary? Whenever such a scenario occurs that I have the essentials for both the events, then the total combinations that will be made in that case, I am prepared in as many ways as I can. I can say, how many shirts did I have, two different types of shirts, how many types of pants did I have, I had three different types of pants, then I would say 2 * 3, what we will do is multiply
by which event the two events of the shirt are possible. There are two types of shirts, there are pants, how many types are there, there are three types, so two out of three, I will say, how many will come to me, if I have made a similar course question in front of you, then walk very carefully while understanding, once I have understood, there
would have been a shirt and there would have been my If there were 5 types of pants , then how many combinations could have been made. You would say: Shirt, Van shirt, Tu shirt, Three shirts, For all four shirts, You can wear it for 5 minutes with the first shirt, Punch pants with the second shirt, All five ways with the shirt. With the pant and the fourth shirt, all the five types of pants, how much is it? 555 You will say 20 Respectfully, if I direct,
then I will say, what are these two events, both are necessary events, so I will have to wear four shirts and punch pants. Total four and punch 20 combinations What can we do here in 20 ways I can get ready to go to the party If I have 20 combinations then I can get ready in 20 ways If I were to ask you in this question
, let's talk a little about it Let's move ahead, what do you have to do, you have to go from Delhi to Ladakh, okay, I have taken an example, there is no direct way to go, what will you have, if you have to go from Delhi to Ladakh, then you
will go through somewhere in between. Where Dehradun will be in the middle, you will have to go to Dehradun first, there is no direct route, either from Delhi you will go to Dehradun or from Dehradun to Ladakh, this is the only possible way to reach there, so we have man, let me talk about the outcomes, man. Lo, I have to go from Delhi to Dehradun, I can go in two ways, either I will go by car or I will go here by bus, it is okay if I talk from Dehradun, if I have to go to Ladakh, then I have three ways or So I will take a bicycle from here, I will go here by bicycle, or
I will go here on foot, or I will get an auto from here, I will go by auto, or I will get a helicopter from here, or I will get an airplane, I will go by airplane, okay, so I have here. What are the routes, if I want to go from Delhi to Ladakh, then first I will have to go to Dehradun. After Dehradun, I will have to go to Ladakh, so either I can go from Delhi to Dehradun or I can choose either of these two routes. I have four ways to reach Ladakh from Dehradun by car or by bus.
If I take any of these ways then in total how many ways can I go from Delhi to Ladakh? You will say Sir, this is also necessary for me because only after reaching Dehradun from Delhi will the further path be covered. It will be done from Dehradun to Ladakh. Ask this is also an accessory for me, so I have two outputs here, four outputs are these, so I have eight ways in which I can reach Ladakh from Delhi. Is this thing available to all the people? Understand
the fundamental principle of counting. Multiplication principle says that when we have what, if I am taking two things, both of them are necessary, then it is okay to do as many cases of the first event as possible . If we multiply all the considerations we are making, we will get the total number of events, okay?
1 can be in MBS and the other can be in ENVEJ, so the total number of ways in which I will do both these events will be as per my understanding, I just have to remember that as it says, I have one more example and I have two water bottles. Okay,
so in how many ways can one take the combination of tiffin box, garden and bottle, you will say, Sir, look, if he is going to school, he has to take the garden with him, it is compulsory, he has to take tiffin also because he will feel hungry during the day and will eat food. So if he feels thirsty , he will also need a water bottle or will have to carry all the three things.
In the school, there was a check in the small classes, the teacher was dying that if he does not take the bag, brother, you will keep it on your lap, there is no tiffin. Will take it and keep it again in the afternoon, I have forgotten the water bottle and will keep it, then if I say that I don't remember this thing, first some teachers scolded the children a lot, now I don't know how to take care of my feet, I am so scared, I am not afraid, so I have all the three events. What are the compulsory things? I have to do all three things. There are two schools and gardens. I can choose first or second. I have three types
of tiffins and I have two types of water bottles. So what will be the total combination if I multiply? Do it 2 * 3 6 * 2 = 12 Okay, there are 12 ways I can do that, if you want to see it in the form of a diagram, I said first I have selected the back, then I will select the bag van or then I will select the bag tu. After that, I have tiffins, first tiffin, second tiffin, third tiffin, I can do things with bag van, back also with you, tiffin van, tiffin,
you can choose tiffin three, okay, these are the combinations, then after that , the water bottle that I have is water bottle. I will take van or water bottle 2, okay Bagwan took t1, after that water became water bottle, you are okay Bagwan, took Pintu, took water bottle, so I can do this, if you get all the combinations, then total 12 possibilities will come to me, so we will do it directly. We had two bags, three different ones, how many water bottles were there, so how many vegetables did I have in total,
how many ways did I have, how many combinations of water bottles and tiffin can a child make, so we will have 12 of them, or this thing has been understood. Let's go next, I have a question, I have these outcomes and records, possible outcomes are there, I have a coin, it has
been tossed three times, what will be the total outcomes, okay, now here, as we pick up the coin, I picked up the coin for the first time, so I have What will come, either heads will come or oil will come. Second time when I take the coin, heads will come again or how many will I have with me. Okay, if I have to calculate the outcomes, how will you count? You said, come on sir, for the first time I got heads. Okay,
so I said for the first time I took heads, here also I got heads, for the third time I took heads, if I got heads then what will be the first outcome, head head, after that I take heads, now it will go in reverse, I considered both heads in the starting, so also like this So it was possible that the one who comes in the third time gets the tail, then I will get the second head, head and tails, okay, now what will happen next, here you will say, sir, what did you say, the first time he gets heads, the second time too he is getting heads like this. It was possible that for the first time head would come and for the second time what would come oil would come
here then head and oil now here again for the third time my head could come oil could come then here would be head and head oil and here oil would be this combination? It is done, after this I will move ahead. Now let us start from the starting. I had said that I had assumed the head in the starting but it was possible that the oil would have gone in the starting itself. If the oil had gone in the starting then you would have said sir about the second head. After that again head then oil head it could have been like this first oil came then head came then again oil came again oil