99% failed this strange Algebra math question| algebra simplification

This is a very strange question, but well, I saw this survey and I decided to share it with you. my subscribers, now first of all, we are familiar with factorial, all right, but the truth is that There are different types of factorials. Okay, now first of all, let's start with the one that we know what factorial means, for example, if we say three factorial, alright? Now, three factorial simply means three times two times one. Four factorial simply means four times three times two times one, okay, that is factorial. Now this double factorial is different from factorial. when you talk about the double factorial, it now depends on whether the number carrying the double factorial is an even number or an odd number now in this case the number that is carrying this double factorial is an odd number, so double factorial simply means for this odd number means the product of all the odd numbers from nine to one or from one to nine, all odd numbers Okay, now for example, assuming we have four factorial, notice that this is what's an even number. so it's going to be the double factorial, sorry, so it's going to be the product of all even numbers from four to one, which will give us what? Four times two, right? Yes, okay. Now look at What we have here is nine factorial, nine double factorial, so we are going to get the product of all odd numbers. numbers from nine down to one, so that means nine double factorial is going to be nine times seven five times three is right, times one, yeah, one is also an odd number, now that is nine, double factorial, do you understand now? That is it for the double factorial. Now, what about this number with # What does that really mean? This means seven primordial. Yes, that is primordial. Now what? the product of all our prime numbers from seven to one or from one to seven, all prime numbers the product of all prime numbers from seven down to one, which means that seven primordial is It's going to be seven times another odd number, and the one before seven is five, right? Another odd number. number, sorry, not odd number, prime number, another prime number that is before five is three, another The prime number that comes before three is two. Note that one is not a prime number. Okay, yes, you can. One is not a prime number, but that is not what we are here for—just know that. These are the prime numbers we have from seven to one; so this is our seven primordial, okay? All right. Now this is where you need to pay very close attention. I mean, this—now, what you have here If you place your factorial sign before your number, it is different from your factorial. but before I explain this, which is called a subfactorial, I'm going to explain factorial in details, because it's when you understand that you will be able to understand this subfactorial now, for example, if we are given these two or three numbers—one, two, three—and we are asked In how many ways can we arrange these three numbers? Notice that we already have the first arrangement, which is one two three; we can decide to keep this. One constant, and swap the positions of these three and two, so we have three and two, I'm. It's going to come down to explaining this one so that we all can follow, okay? So I'm coming down now. All right, have you subscribed to this channel? If not, please click the subscription button. Turn on your notification bell so you don't miss our amazing videos—we upload new videos every day. We share interesting videos, we share interesting topics. Okay, so please always tune in at your Convenience to watch our new upload and give us a thumbs up if you're actually enjoying this video Now back to what we were doing—we are still arranging one, two, three, to the greatest extent possible. Many ways we can write, so we have kept one constant and interchanged three and two. Now we are going to keep two constants. Now, if we keep two constants, we have one and three here. Right now, if we still keep two constants, we can interchange three and one, and that is all we can do. Do with two being the first; now let's pick three. If we keep three constants, we interchange one and Two, okay, one and two—we write one and two, or we can keep three constants and interchange two and One, so you notice that we can actually arrange these three letters or these three numbers in six. six ways, okay. Now this is factorial, so this means that if you have three items, this is the way You can arrange them in six ways; now, assuming you already know this, this is factorial. The best way to solve this is instead of trying to figure out how many ways you can solve it this way. You can arrange it this way, just using three factorial, okay? Now remember three factorial. because we have three numbers, so it's three factorial, which is three times two times one, which will give us six, can you see? Very easy now, when we talk of subfactorial, now assuming the question Is three subfactorial acceptable? Three subfactorial, assuming that is what we are being asked for in subfactorial. you are asked in how many ways can you arrange these three numbers in such a way that None of them will retain their original position now. Let me explain. When you look at this notice, That one is returning the first position in the original arrangement; two is returning the second. Position three is returning the third position now. Subfactorial is saying we don't want anyone. That is repeating its position; okay, that's retaining its position. Now look at this one. The first number here, and this is also the first number here, so these two are not subfactorials. We are not going to use them because one is returning its position, the first position now. Look at this—these two are returning their position; they're not maintaining their position here, right? Na1 Chandi the first yeah. Beware the series of tennis position You can see that prit is returning these positions. So you know you're going to use it. Then let's move on to this tool, which is now maintaining its position. Good three is now that into each now. What is your current mood? Is it returning to him or is it now in position? Good, so this is such a factor. This is what we are looking for Now let's check: this one is not returning, one is now retaining, and two is not retaining. so this is also going to be taken now look at this three is not retaining its position but Two is retaining its original position, so this is not taking place; thus, it means That the subfactorial of three will simply give us two as our result— is that clear now? Let's proceed. Back to what we are looking for. Now, what is the formula for this subfactorial? For example, this. sub factorial this sub factorial we are going to have is equal to three factorial multiplied by so we have one over zero factorial plus one over one factorial okay sorry minus one over one factorial, okay, then this thing you got plus one over, we start at one factorial, two factorial minus one over three factorial, and that is it. Now we are going to stop at three factorial because We have three items to arrange. Do you understand now? Let's solve this and see if we are going to. Get the two that we initially obtained when we did it manually, okay? So this is still manual, anyway, but which has this formula, so it means that our three subfactorial will be equal to one over now zero factorial is one minus one over one right plus now one over two factorial is two minus one over Remember, your three factorial is three times two times one, which is six. Okay, so it's going to be That's fine now let me draw this line so that we will know what we are doing, all right Now let's continue. Now three sub factorial is going to be one minus one, which is zero, so what we have One over two minus one over three. Remember, we are going to multiply this by three. factorial, let's not forget — so we have three factorial brackets now, let's make this to be six as well, so this is two times three times three, okay? So one times three is three, two times three is six minus one over six, so we have that three subfactorial is three factorial multiplied by Three minus one is two, and six is a common term now—remember that three factorial is six, right? three times two times one, so our three sub factorial is going to be six multiplied by two Over six, so we're going to get two. Can you see? We got the same results now that you understand. Very well, what a subfactorial is. Let's go back to our question. Have you given us a thumbs up? and I know you know that this is not an ordinary math question, so I would appreciate it if you can share this so that other people will learn just like I learned so that other people will Learn, and I'm sharing it with you, okay? All right, now let's go ahead. Now let's talk about five sub- factorial okay okay this will be five factorial bracket remember our formula is going to be one over zero factorial minus one over one factorial okay plus one over two factorial Okay, minus one over three factorial. Let me stand here. All right, then plus one over four factorial. minus one over five factorial, remember that we are stopping at five because this is what five subfactorial now this is equal to five factorial bracket this is one over one minus one over one as well plus this is one over two minus one over three factorial is three times three okay let me write them here three factorial is three times two times one which will give us six now four factorial is equal to four times three times two times one which is equal to 24 Four times three is twelve, twelve times two is 24, so we have 24 now. Five factorial. is equal to five times four times three times two times one, which is equal to, I don't know if I'm now fast, I promise I won't be fast so that we all can follow, okay? Now, five times four is 20, 20 times Three is 60. 60 times two is 120. 120 times one is 120. So we have 120 now. Let's substitute now. one over three factorial, three factorial is six, okay. All right, now plus one over four factorial is 24 all right minus one over five factorial is 120 all right now let's continue let's do the Let's eliminate as much as we can so we have five factorial times one minus one, which is zero, so this one We are going to multiply this by three and this by three so that we have one. they will indeed share the same denominator, and now, when it comes to this, for them to share We multiply 24 by 5 to get 120, and we also multiply this by 5 to get 5. So we have 5 times 5, so it's going to be plus 1 times 5, which is 5, 24 times 5 is 120, minus 1. Alright, so we calculate 5 factorial divided by 3 minus 1, which gives us 2 over 6, right? Then plus 5 minus 1. We give us 4 over 120, okay, so we are getting close to the solution, but before that, let me Write outGlobals 9 multiple哈尔滨 9 times 7 times 5 times 3 Okay, so let me write it somewhere: 9 double factorial is 9 times 7 times 5 times 3 and 7. primordial 7 primordial is 7 times 5 times 3 times 2 okay all right so that I can clean this and then continue with what I'm solving, all right? Have you given us a thumbs up now? Remember that. We are still trying to get 5 subfactorial. Okay, now this is equal to 5 factorial in brackets. So what we have here is 1 over 3 plus this will give us when 2 divided by 4, we have 2. When it divides this, we have 60, okay. All right, now let us solve 3 and 60. Let's bring them to the same denominator, okay, so it's going to be 3 times 20, right? So we multiply this by 20 and Multiply this by 20 as well, so it's going to be 1 times 20, which is 20, 3 times 20 is 60, plus 2 over 60. Alright, okay, yes, now we have this is equal to 5 factorial, bracket, okay, 20 plus 2 gives us 22. Over 60, so this is what we have now. What is our 5 factorial? Remember that our 5 factorial is 5. 4 times 3 times 2 times 1, and that will give us what—120—that is what we got: 5 times 4. Is 20? 20 times 3 is 60. 60 times 2 is 120. So this is what we have: 5 sub factorial is going to be 120. multiplied by 22 over 60, so 5 sub factorial is going to give us 2, right? 60 divides 120, we give US 2, so we have 2 times 22, we give us 44. Amazing, right? Now it's time to bring everything together. and solve this strange math problem; now we have obtained our 5 subfactorial to be equal to 44 let Now let's clean everything and substitute our values, okay? Now remember that our 9 sub factorial Is 9 times 7 times 5 times 3 right divided by our 7 primordial is 7 times 5 times 3 times 2, okay? then multiplied by our 5 sub factorial is 44, okay, so this is equal to 7, we divide it by itself Give us 15, we divide it by itself to get 1. We divide 1 by 3 to get 1/3. We divide 1/3 by itself to get 1. So what we have is 9. over 2 multiplied by 44 over 1, now, until we divide this to give us 22, right? So what we have Is 22 multiplied by 9? 9 times 2 is 18, right? 8, carry 1. 9 times 2 is 18 plus 1 is 19, and this Is the answer to the strange question? I hope you learned something new today. Please share. All right, comment and let me know what you have to say about this, or do you have another way of doing it? Solving this, I will be glad to learn from you. Thank you so much for watching, and see you in My next video, bye