Factorials shortcuts - Free Educational videos for Students in K-12

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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