– [Voiceover] So let’s ask ourselves some interesting questions about

alphabets in the English language. And in case you don’t remember and are in the mood to count,

there are 26 alphabets. So if you 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 Z,” you’ll get, you’ll get 26, 26 alphabets. Now let’s ask some interesting questions. So given that there are 26 alphabets in the English language, how many possible three letter words are there? And we’re not going to be

thinking about phonetics or how hard it is to pronounce it. So, for example, the word, the word ZGT would be a legitimate

word in this example. Or the word, the word, the word SKJ would be a legitimate

word in this example. So how many possible three letter words are there in the English language? I encourage you to pause the video and try to think about it. Alright, I assume you’ve had a go at it. So let’s just think about

it, for three letter words there’s three spaces, so how many possibilities are there for the first one? Well, there’s 26 possible

letters for the first one. Anything from a to z

would be completely fine. Now how many possibilities

for the second one? And I intentionally ask this to you to be a distractor because

we’ve seen a lot of examples. We’re saying, “Oh,

there’s 26 possibilities “for the first one and maybe

there’s 25 for the second one, “and then 24 for the third,”

but that’s not the case right over here because

we can repeat letters. I didn’t say that all of the

letters had to be different. So, for example, the word, the word HHH would also be a legitimate word in our example right over here. So we have 26 possibilities

for the second letter and we have 26 possibilities

for the third letter. So we’re going to have, and

I don’t know what this is, 26 to the third power possibilities, or 26 times 26 time 26 and you

can figure out what that is. That is how many possible three letter words we can have for the English language if we didn’t care about

how to pronounceable they are, if they meant anything

and if we repeated letters. Now let’s ask a different question. What if we said, “How many

possible three letter words “are there if we want

all different letters?” So we want all different letters. So these all have to be different letters. Different, different

letters and once again, pause the video and see if

you can think it through. Alright, so this is where

permutations start to be useful. Although, I think a lot

of things like this, it’s always best to reason through than try to figure out if

some formula applies to it. So in this situation,

well, if we went in order, we could have 26 different

letters for the first one, 26 different possibilities

for the first one. You know, I’m always

starting with that one, but there’s nothing special

about the one on the left. We could say that the one on the right, there’s 26 possibilities, well for each of those possibilities, for

each of those 26 possibilities, there might be 25 possibilities for what we put in the middle one if we say we’re going to

figure out the middle one next. And then for each of these

25 times 26 possibilities for where we figured

out two of the letters, there’s 24 possibilities

because we’ve already used two letters for the last

bucket that we haven’t filled. And the only reason I went 26, 25, 24 is to show you there’s nothing

special about always filling in the left most letter or

the left most chair first. It’s just about, well,

let’s just think in terms of let’s just fill out

one of the buckets first. Hey, we have the most

possibilities for that. Once we use something up,

then for each of those possibilities we’ll

have one left, one less for the next, the next bucket. And so I could do 24 times 25 times 26, but just so I don’t fully confuse you, I’ll go back to what I have been doing. 26 possibilities for the left most one. For each of those, you

would have 25 possibilities for the next one that you’re

going to try to figure out because you already used one letter and they have to be different. And then for the last

bucket, you’re going to have 24 possibilities, so this is going to be 26 times 25 times 24, whatever that happens to be. And if we wanted to

write it in the notation of permutations, we would

say that this is equal to, we’re taking 26 things, sorry, not two p. 20, my brain is malfunctioning. 26, we’re figuring out how

many permutations are there for putting 26 different things into three different spaces and this is 26, if we just blindly apply the formula, which I never suggest doing. It would be 26 factorial over 26 minus three factorial, which would be 26 factorial over 23 factorial, which is going to be

exactly this right over here because the 23 times 22 times

21 all the way down to one is going to cancel with the 23 factorial. And so the whole point of this video, there’s two points, is one,

as soon as someone says, “How many different

letters could you form” or something like that, you don’t just blindly do permutations or combinations. You think about well, what is

being asked in the question. Here, I really just have to

take 26 times 26 times 26. The other thing I want to point out, and I know I keep pointing it out, and it’s probably getting tiring to you, is even when permutations are applicable, in my brain, at least,

it’s always more valuable to just try to reason through the problem as opposed to just saying,

“Oh there’s this formula “that I remember from weeks or years ago “in my life that had an N

factorial and K factorial “and I had to memorize

it, I have to look it up.” Always much more useful

to just reason it through.

26 alphabets? Letters*?

Nice brain teaser.

15,600

Perfect!

Skj sounds like something Hank Green from Crash Course would have as one of his words.

But what will be the probability? Sample space will be 26*26*26 and event will be 26*25*24

Thank you very much! 🙂

KYW!!

the word HHH is my favorite word!!!

HHH

lol, 26 alphabets

I just came here to commend you, Sal, on your impressively quick utterance of the English alphabet. In the highly competitive world of fast-alphabet performance, you are a god amongst 1st graders.

I have the word (TESTIM) and want to know how many 3 letter words can I form without repeating a letter

It is the formula n^p where n is number of numbers, letters… and p is number of positions.

any one can solve my issue

There are two projects for a company to complete,project x and project y.There are 16 employees to be assigned to the two projects. If eight of the employees will be assigned to project x and eight to project y.How many different project teams are possible?

solve this statement and tell me answer as soon as possible.

There are 26 letters in the English alphabet

Quick question… If the question were to find the number of ways the make 7 letter words such that no 2 consecutive positions can have the same letter would the equation become 26 X 24 X 24 X 24 X 24 X 24 X 25 = 215,654,400?

Great teacher

Hey Khan, When you were changing the number of letters you were doing 23x25x26. My teacher said order does matter. Why?