Factorials shortcuts - By tecmath
Transcript
00:0-1 | Good day , Welcome to Tech Mouth channel . What | |
00:01 | we're going to be having to look at in this | |
00:02 | video is factorial . What are these guys or these | |
00:06 | you would have seen before ? Probably written like this | |
00:08 | . Um , or maybe you've just seen the special | |
00:10 | button on your calculator . So things like five Factorial | |
00:13 | here and what they are is pretty much where you're | |
00:17 | getting every number , every whole number below the number | |
00:20 | of 554321 And you're multiplying to find the product of | |
00:25 | these . Okay , so five times four times three | |
00:30 | times two times one is what ? Five factorial is | |
00:33 | Okay . Which is equal to 120 . And these | |
00:38 | guys are used a whole lot when we're looking at | |
00:40 | combinations and permutations . Also a little bit in Algebra | |
00:43 | as well . And what are they were pretty much | |
00:45 | at its most basic you have , if you can | |
00:47 | imagine five different things , we could arrange them 120 | |
00:52 | different ways . So it's an expression of how many | |
00:54 | different ways we can order this many objects . Okay | |
00:57 | , so if you were to say there is n | |
00:59 | objects , N factorial would be the number of ways | |
01:03 | you can actually order these . So by the way | |
01:06 | you also have this one which is zero factorial . | |
01:09 | Just going to mention this right now , zero factorial | |
01:12 | is equal to one And this is going to throw | |
01:14 | you a little bit because you're gonna wait hey on | |
01:16 | what ? 0 ? How would you even write that | |
01:19 | ? Um This is just one of these things . | |
01:20 | I'm not going to get too much in the explanation | |
01:22 | . I've heard this explained is how many different ways | |
01:24 | could you order the number zero or order as an | |
01:28 | empty set ? And you only have one way of | |
01:29 | doing it . But the mainly where we really worry | |
01:32 | about this is because it's used labor to actually make | |
01:34 | a few combination . Permutation calculations actually work . Okay | |
01:37 | , so just as long as you can sort of | |
01:39 | keep that as a side . So I tend to | |
01:41 | know now , I'm just gonna go through a few | |
01:43 | different types of factorial questions . Okay so a couple | |
01:48 | to start off with , let's start some easy ones | |
01:50 | . What is four factorial ? So this is four | |
01:56 | times 3 times two times one And this is equal | |
02:01 | to 24 . Okay , so we got a bit | |
02:03 | of a harder one now and what he wants to | |
02:05 | ask you what five factorial divided by three factorial is | |
02:13 | launch straight into those because I think you can get | |
02:15 | the idea of what each one of these is . | |
02:16 | So how would you go about working this out now | |
02:19 | ? And it's the most basic what we could do | |
02:21 | is we could just Expand these out , we could | |
02:23 | say five Times four times 3 times two times one | |
02:29 | , but I'm gonna show you a few little tricks | |
02:30 | , we're doing a couple of short cuts on this | |
02:33 | . So the three factorial could be three Times two | |
02:36 | Times 1 . So what you're going to notice here | |
02:39 | is that these guys here , the three the to | |
02:43 | the one they cancel each other out because there's one | |
02:46 | down here , you see that ? So we just | |
02:47 | left with five times 45 times for the answer equals | |
02:51 | 20 . But I want to show you a little | |
02:54 | secret , a little little shortcut for this , which | |
02:56 | is this ? So , so I think about my | |
02:59 | five factorial . I could think about this also being | |
03:02 | like this , I can think about it being five | |
03:05 | times four times three factorial cause three factorial is three | |
03:10 | times two times one . That saves writing that out | |
03:12 | . And three factorial is three factorial . So you | |
03:15 | can just straightaway council these ones out . So you | |
03:20 | can almost just ignore that and just go with his | |
03:22 | first to , you know , the five in the | |
03:23 | 4 to 5 times four equals 20 . What about | |
03:27 | I give one that you can try . What about | |
03:30 | 70 factorial ? Over 68 factorial . And you don't | |
03:36 | want to put one of these in the calculator a | |
03:37 | lot of time because you get a big error message | |
03:39 | . So it's really handy to use this little trick | |
03:42 | rather than working at 70 times 69 times 68 times | |
03:45 | 67 times and getting some huge number . We can | |
03:48 | use that little shortcut and we can do this right | |
03:50 | , we can go . So we can be like | |
03:52 | 70 times 69 And this is going to be and | |
03:57 | I'm going to write this in a different color because | |
03:59 | I wouldn't even bother right this on occasionally . This | |
04:02 | is times 68 factorial And this is going to be | |
04:05 | over 68 factorial . Yeah , but I could have | |
04:08 | not even bothered put those together because they're just going | |
04:11 | to cancel each other out and then they're gonna disappear | |
04:13 | . So we can just be left with 70 times | |
04:17 | 69 , 70 times 69 . Or the answer to | |
04:19 | that is going to be 4830 . Okay . All | |
04:24 | right . What about a different type of question with | |
04:26 | these ? I'm going to go a bit of a | |
04:28 | different type of one that you might get . What | |
04:30 | about we try five factorial Over three factorial , two | |
04:35 | factorial . That's a 23 factorial times two factorial . | |
04:39 | And what does that equal ? Yeah , I'm just | |
04:42 | going to launch straight into how I worked this out | |
04:44 | in a nice short hand sort of way because five | |
04:47 | factorial , three factorial . What I did before I'm | |
04:50 | going to end up with five times four . All | |
04:53 | right , because the rest of it's going to be | |
04:55 | times three times two times one . But that's gonna | |
04:56 | be taken care of here . Yeah . So we're | |
04:59 | not gonna even bother put that in and this party | |
05:02 | is two factorial two factorial is too Times one . | |
05:05 | Someone's going to put it to their because two times | |
05:07 | one is two . So we ended up with five | |
05:10 | times four , which is 20 and two . It's | |
05:15 | too 20 divided by two . The answer is 10 | |
05:20 | . What about we try 12 factorial over 10 factorial | |
05:27 | Times two factorial . What about you give this one | |
05:30 | to go and see how you go And hopefully what | |
05:33 | you're going to do and see if you can do | |
05:34 | this in a shortcut method . Hopefully you've paused it | |
05:36 | now . And then in the India you've tried it | |
05:38 | this 12 factorial over 10 factorial . Is this going | |
05:41 | to leave us with 12 times 11 ? Because then | |
05:45 | the rest of it's going to be counseled out correct | |
05:47 | ? Yeah . You got that idea because that's going | |
05:48 | to be 12 times 11 times 10 facts when we | |
05:50 | got rid of it . And two factorial is just | |
05:53 | too . So What are we left with ? 12 | |
05:57 | times 11 over to this is going to be equal | |
05:59 | to 132 Over two , which is equal to 66 | |
06:05 | . All right now , that is the start of | |
06:08 | factorial . We're gonna be using these in later videos | |
06:11 | in a combination of permutation calculations . So I thought | |
06:14 | we should do a video and and have a look | |
06:16 | at the video based on those first anyway . Hope | |
06:19 | you found that video useful . See you next time | |
00:0-1 | . |
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Factorials shortcuts is a free educational video by tecmath.
This page not only allows students and teachers view Factorials shortcuts videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.