Arrange Digi-sign Order with airSlate SignNow

Arrange digi sign order

I spilled some Seltzer on myself just a moment ago so sorry if I look like a doofus so how many four digit codes can we create using the digits 0 through 9 well it depends it depends on what restrictions are set if any are we allowed to repeat digits or are we not allowed to repeat digits we'll get numbers for both possibilities in today's wrath of math lesson I encourage you to sit back relax a little bit you know grab a cup of hot chocolate or something it's the holiday season we got we got the Christmas tree we got a we got the Santa hat and it's my first lesson using my new wireless microphone setup so I'm a free man I can spin around do a ballet routine whatever I want but I want to do math so that's what we're gonna do so how many 4 digit codes can we create using the digits 0 through 9 and let's say allowing repetition to start off with first important question to answer is how many digits is that 0 through 9 how many possibilities well that is precisely 10 total digits 0 through 9 that's a total of 10 digits and then we want to know how many 4 digit codes can we create from these 10 digits if we're allowed to use the same digit multiple times well some number of our code has to be first some digits got to go there there's 10 total possibilities any of these 10 digits then what about for the second number in our code well there's still 10 possibilities because we're still allowed to use any of those 10 digits now to count up all of these possibilities we need to multiply because for every one of the 10 digits that could go first there are 10 digits that could go second so we're going to need to multiply to total up all those possibilities then same thing it's pretty simple for the for the third number in the code there's 10 possibilities any one of these 10 digits same thing for the fourth number and so the total number of four digit codes using the digits 0 through 9 and allowing repetition is 10 to the power of 4 or if you prefer 10,000 you can use very similar reasoning very similar problems for example what's the number of say seven digit codes using the digits 0 through 9 and allowing repetition well it's going to be the same thing 10 times 10 times 10 times 10 but 7 times because there's 1 2 3 4 there's gonna be seven total numbers in our code because we're talking about a 7 number code right now so the total number of possibilities would be 10 to the power of 7 another similar problem would be how many 5 digit codes are there using the digits 0 through 4 and allowing repetition well how many digits are here how many digits can we choose from 0 1 2 3 4 that's 5 digits so how many five-member codes can be created from those 5 digits well that would be 5 to the power of 5 because 5 digits can be in the first spot 5 digits can be in the second spot 5 digits can be the third spot and so on so you know by thinking about one problem solving that one problem we can use the same reasoning over and over again in a bunch of other situations so let's go ahead and switch the problem to not allowing repetition and see how that plays out all right so how many 4 digit or 4 number codes can be created using the digits 0 through 9 not allowing repetition it's a pretty similar problem but it's got a bit of a different solution some digit has to go first in our code and there are 10 possibilities we could put any digit first but things get a little different for the second number in our code we no longer have 10 options because whatever digit went first we can't use it again because we're not allowing repetition so now there are only 9 possibilities for the second digit then for the third digit there are now eight possibilities left because we can't use either of the two digits that were in these first two spots and then for the last number in our code we've only got seven digits left to choose from and so this totals up to let's see 10 times 9 is 90 90 times 8 is 720 720 times seven is 5040 so a total of 5000 40 possible 4 digit codes using the digits 0 through 9 and not allowing repetition and in this case this turned out to be a little more than half of the total number of codes that could be created when we did allow repetition which you might remember was 10 to the power of 4 or 10,000 so this is a little bit more than half of that now this could also be solved using what is called the permutation formula often written like this P in this case it would be P of 10 comma 4 this is the number of ways of ordering 4 objects 1 2 3 4 from a collection of n objects which is what we've got here a collection of 10 digits and we're ordering 4 of them to create a code and implicit in this formula is that repetition is not allowed we're not allowed to use the same digit in multiple times this formula happens to be equal to 10 factorial divided by 10 minus 4 factorial which if you simplify these factorials you'd end up with 10 times 9 times 8 times 7 of course in general of course this formula the number of permutations of our objects from a collection of n objects is equal to n factorial divided by n minus R factorial and I've got a pretty good lesson on that so I'll leave a link to that in the description you can go check out and see some more examples of this formula and a thorough explanation of why it works all right let's do just one more quick practice problem with not allowing repetition let's say let's say we want to count the number of 4 digit codes we can create from the digits 0 through 5 not allowing repetition so again we're creating we're creating four digit codes and we're not allowing repetition using these six digits well for the number that goes first there are six possibilities man that plane is really loud I don't know how much the mic is picking it up but it is loud for the for the second digit there are five possibilities because we can't repeat the digit that went first so there's only five possibilities for the second number in our code and then similarly for the third number in our code we had six digits to choose from originally but we can't choose the first one again we can't choose the second one again so now only four digits remain to choose from and then there's only third digits to choose from for the last number in the code this comes out to be 6 times 5 is 30 30 times 4 is 120 120 times 3 is 360 that's the number of 4 digit codes that can be created using the numbers 0 through 5 and not allowing repetition so I hope these few examples helped you get a better idea of how to solve these sorts of problems we'll do some trickier examples in another lesson let me know in the comments if there are any particular examples you'd like to see me work through in another lesson but to try on your own an example problem to try on your own count the number of four digit codes that can be created using only even numbers and let's say not allowing repetition so you're counting the number of four digit codes using only even numbers so 0 2 4 6 and 8 and not allowing repetition see see what you come up with and I'll leave this solution in the description let me know in the comments if you have any questions need anything clarified or have any other video requests thank you very much for watching I'll see you next time and be sure to subscribe for the swankiest math lessons on the internet if you didn't see the most recent a fire hip-hop track I dropped be sure to check that out MC Shawn E in today's video will spit bars so hard but if you stood not too far they give you a free ride to Mars my words are so hot that you mistake him for stars okay or deep inside above the planets fiery course alright the math video and help de Broglie test scores calculus logic improves I can graph 3 probability more somebody coming