How To Sign Mississippi NDA

How to document type sign nda mississippi

how many ways can we rearrange the letters in a word and sometimes it's called the mississippi problem how many ways can you rearrange the word mississippi that's typically the go-to problem in a textbook in the united states but you know pause the video see if you can figure out mississippi we're going to start with some smaller ones to begin with and you know how would you tackle the problem maybe that's why you're here it's because you don't know so here we go start with one that's a lot simpler we'll start with my name dan a three letter word and we'll rearrange it um all the different times we'll the first method is brute force mississippi would be tough to do brute force and what i mean by brute force is we just list them all out so um you know dan there's one way you could go dna dna so there's word the the d is in the in the front then we could put the a in the front and so it would be a d n and that should be an upper case because i'm using upper case or a n d uh or we could put the n in the front so now the n's in the front and so n a d that should be a d or n d a and that exhausts our list so that's all six of them and that would just be solving it brute force if we can just list them all out there they are we know they're six so but let's look at it in terms of fundamental counting and maybe a tree diagram also so with the fundamental counting theorem and i encourage you to go look at a video or two of that with fundamental counting theorem but what i like to do is i like to put everything in bins and there's three letters and we have to use all the letters so we have three bends in the first bin we could put three uh three letters it could be a d it could be an a or it could be an n which leaves if so if we pick one of those letters that means for the second band there's only two and for the third bin there's only one and so the fundamental counting theorem would be three times two times one or six uh you know and what that is when you multiply the numbers starting from the largest from from the number and then going down and multiplying them all out that's called a factorial and so we often in mathematics represented as three with an exclamation point so factorial okay and so that's looking at it in bins so now let's look at in in a tree diagram in a tree diagram we would have three choices to begin with we could either have a d an a or an n okay then once we choose a choice then we can have two more choices so we could have an a or an n here and then after we choose that we only have one choice so if we chose d and a then n is the only one left and if we want d and n then a is the only one left and then the same with a so a you could either have a d or an n and then once you pick that there's only one left which would be an n here and a d here and the same with n we could either have a or d and then it would be d here and then we only have an a left for here and if you count each of these there's one two three four five six it's kind of like brute force but that just shows you another method of looking at it and some people just need that so there's six ways so we've kind of beat this problem to death there's three different ways of solving it those are some some skills you can put in your toolbox if you've never seen those before and they work great for a lot of different counting counting problems so let's ramp it up what about the word walk so now we have a four letter word and i like the fundamental counting theorem that's kind of my favorite i like to look at these in terms of bins and so there's one two three four bends walk has four letters and so we'd know on the first letter uh first bin there could be four choices we could put a w an a an l or a k there once we choose one now there's only three left to choose once because we're not repeating any of these letters it's going to remain a four letter word then two and then one and so that would be four factorial or 4 times 3 times 2 times 1 or 4 times 3 is 12 times 2 which is 24. so walk you could if you had to do it brute force you could write out 20 you'd have to write out 24 different words for the word walk w-a-l-k all right let's let's go to the next level all right so what about the word cool now here is another four letter word like walk and so you might think immediately that that we have you know one two three four four three two one so another four factorial uh number which is 24 4 times three times two times one because we have four letters in cool the problem with that is the letter o occurs twice and so and we can't distinguish between from one o to the other o and so we're this 24 is way too high because we've got some repeaters happening and so let me give you a what this looks like so i have it conveniently i color coded them and i just did a couple of them because i don't want to list out 24 of them but but if you look at these first two here that would be if we colored one of the o's red and the other one blue you know if you're colorblind i'm sorry we'd have to put in different shapes or something but or maybe they're just slightly shaded different for you but we've got we've got two choices for for that if we can change the o's somehow well they're indistinguishable so this second one is the same as the first one so we'd have to divide it out and each one if you look see if we put the cl in front we'd also have two so we're gonna have to divide by the two ways to rearrange that o and so it's not just 24. it's it's uh 24 divided by 2 which is 12 because we're going to cross out all of the all of the repeating o's so there's only 12 here and and then i'll i'll show you on the next one too it gets it we'll make it we'll make a non-word and make it kind of interesting so let's look at a slightly different word you know how this is not a word cool with too many o's but how many ways can you rearrange the word cool and again um now we've got five letters you know you've got the three o's and the c and the l so we have five whole letters the problem with this is again the o's are indistinguishable so you might think it's you know one two three four five bends and five times four times three times two times one um you might think it would work the same way which is five factorial but we're going to have to divide out by all the different ways that we could rearrange those three o's because those three o's again are indistinguishable and so let's take a look at that and i just didn't want to list them all out because there would be a bunch of them but there i listed out two orientations i listed out if we put the l here and the l in front and switched them and if here they're indistinguishable but this shows you all the different ways if the o's were three different colors and it mattered how the different how many different ways we could rearrange those and if you noticed there's six of them so one two three four five six so there's six ways to rearrange three things in a line and uh and that's kind of the same fundamental counting theorem idea uh three times two times one three times two times one gives you six so we have to divide each of these by six and so if we go back to our problem then whoops wrong one if we go back to our problem then five factorial would be divided by three factorial for the three ways to to or the six ways to rearrange cool so so just kind of doing the work here 5 times 4 times 3 times 2 times 1 divided by 3 times 2 times 1 well 1 divided by 1 is 1 2 divided by 2 is one three divided by three is one and so we're left with just five times four which is 20 ways so this strange word cool has 20 ways that you could rearrange it authentically without with the o's being indecipherable all right so we're about done here we're ready for mississippi i think so back to where we began with mississippi maybe now you can figure this out i mean pause it if you're if you think you got it but if you look at this there are 11 letters in mississippi so if we counted that that would be 11 factorial bands however if you notice there are four s's so there are four ways to rearrange the s's so we would divide out those four different s's that are the same we've got four i's that are indistinguishable so we'll have to divide out by the i's and we have two p's so there's two ways to represent those p's so our final answer would be this which be 11 factorial divided by 4 factorial divided by 4 factorial divided by 2 factorial and that would be 11 times 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 divided by 4 3 2 1 four three two one and two one and obviously the ones you can eliminate uh and ignore but i like to put them in there and so then we can start crossing stuff out and i'll change colors here and so two and two crosses out uh two and four would cross out leaving a two there three and three cross out 4 and 8 would cross out leaving a 2 there a 4 would cross out with this 2 and this 2 because that's 4 divided by 4 2 and 6 leaves a 3 there and then 3 and 3 cross out and so you're left with 11 times 10 times 9 times a not nope we crossed 8 out times 7 times 5. and so you get your calculator out and you type that thing in and i think we would have unless i'm pretty sure this is right but you can sure double check me 34 650 ways to rearrange the word so mississippi four thousand six hundred and fifty ways to rearrange this particular word i think a quick google search also finds that i uh but if you're wanting an explanation that's the best i can do hope this helps see you next time ask me a question i'm sure i'll be able to get around and answer it for you thanks a bunch