- so let's ask ourself some exciting questions aboutalphabets in the English language. And in case you don't remember and also are in the mood come count,there space 26 alphabets. Therefore if friend go, "A, B, C,D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S,T, U, V, W, X, Y, and also Z," you'll get, you'll acquire 26, 26 alphabets. Currently let's ask some amazing questions. So given that there space 26 alphabets in the English language, how many possible three letter words space there? and we're no going to bethinking about phonetics or how tough it is to express it. So, for example, the word, the word ZGT would be a legitimateword in this example. Or the word, the word, the word SKJ would be a legitimateword in this example. So how many possible three letter words space there in the English language? ns encourage you to stop the video and try to think about it. Alright, i assume you've had actually a go at it. So let's just think aboutit, for three letter words there's three spaces, for this reason how many possibilities are there for the first one? Well, there's 26 possibleletters for the first one. Anything indigenous a come zwould be completely fine. Now how plenty of possibilitiesfor the second one? and I purposely ask this come you to it is in a distractor becausewe've watched a most examples. We're saying, "Oh,there's 26 possibilities "for the very first one and also maybethere's 25 for the 2nd one, "and then 24 because that the third,"but that's no the situation right over below becausewe deserve to repeat letters. I didn't speak that all of theletters had to it is in different. So, because that example, the word, words HHH would also be a legit word in our example right end here. So we have actually 26 possibilitiesfor the second letter and we have actually 26 possibilitiesfor the third letter. Therefore we're going to have, andI don't know what this is, 26 to the 3rd power possibilities, or 26 time 26 time 26 and also youcan number out what that is. That is how many possible three letter indigenous we deserve to have for the English language if us didn't treatment abouthow come pronounceable castle are, if they meant anythingand if we repetitive letters. Now let's questioning a various question. What if we said, "How manypossible three letter indigenous "are there if us wantall various letters?" for this reason we want all various letters. So this all have to be different letters. Different, differentletters and also once again, pause the video and watch ifyou deserve to think it through. Alright, for this reason this is wherepermutations begin to it is in useful. Although, i think a lotof things choose this, it's constantly best to factor through than try to number out ifsome formula uses to it. Therefore in this situation,well, if we went in order, we could have 26 differentletters for the first one, 26 different possibilitiesfor the very first one. Friend know, I'm alwaysstarting v that one, but there's nothing specialabout the one on the left. We can say the the one ~ above the right, there's 26 possibilities, well because that each the those possibilities, foreach that those 26 possibilities, there can be 25 possibilities for what we put in the middle one if we say we're walking tofigure the end the center one next. And also then because that each the these25 time 26 possibilities for wherein we figuredout 2 of the letters, there's 24 possibilitiesbecause we've currently used two letters because that the lastbucket that we haven't filled. And the only reason ns went 26, 25, 24 is to display you there's nothingspecial around always pour it until it is full in the left many letter orthe left many chair first. It's simply about, well,let's simply think in regards to let's just fill outone that the buckets first. Hey, we have the mostpossibilities for that. When we use something up,then because that each of those possibilities we'llhave one left, one less for the next, the following bucket. And so I could do 24 time 25 times 26, however just so i don't fully confuse you, I'll go back to what I have actually been doing. 26 possibilities because that the left most one. For each of those, youwould have 25 possibilities for the following one that you'regoing to shot to number out because you currently used one letter and also they need to be different. And also then because that the lastbucket, you're walking to have actually 24 possibilities, so this is going to it is in 26 times 25 time 24, everything that happens to be. And if we wanted towrite that in the notation that permutations, we wouldsay the this is equal to, we're taking 26 things, sorry, not 2 p. 20, my brain is malfunctioning. 26, we're figuring out howmany permutations are there for placing 26 various things into three various spaces and also this is 26, if we simply blindly apply the formula, which ns never suggest doing. It would certainly be 26 factorial end 26 minus 3 factorial, which would certainly be 26 factorial end 23 factorial, which is going to beexactly this appropriate over here since the 23 times 22 times21 every the means down come one is going come cancel v the 23 factorial. And so the whole point of this video, there's 2 points, is one,as shortly as who says, "How many differentletters could you form" or something choose that, girlfriend don't just thoughtlessly do permutations or combinations. Friend think about well, what isbeing inquiry in the question.


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Here, ns really just have totake 26 times 26 time 26. The other thing I want to allude out, and I understand I keep pointing it out, and also it's probably acquiring tiring come you, is even when permutations space applicable, in mine brain, at least,it's always much more valuable to just shot to factor through the trouble as protest to just saying,"Oh there's this formula "that ns remember indigenous weeks or years back "in my life that had an Nfactorial and K factorial "and I had actually to memorizeit, I have to look that up." always much an ext usefulto just reason it through.