Fax Initials Arrangement with airSlate SignNow

Repeat initials order

all right in this video I'm going to do an example involving permutations that have repeated symbols and what we're going to do kind of a classic problem we're going to look at how many different linear Arrangements from the letters from the word Mississippi are there and again the idea is you know for example we've got four SS here the SS are all going to be indistinguishable okay so that's that's one thing that's important so the formula says well if there are in objects total so in this case the number of objects is going to be the number of letters so we've got one two three four five six seven eight nine ten looks like eleven letters so in this case we've got eleven objects that we're looking at okay that we're working with it says if you've got n objects in sub one of a first type in sub 2 of a second type in sub R of the Arth type it says if you add the types together well you should get in so all that means here is you know the different types of objects we have well we have different types of letters we've got em we've got M's present or at least one of those we've got an eyes in there we have S's in there and it looks like we have peas in there as well and I think that's it so those are the different types and we're just going to count we've got one M let's see we've got one two three four four eyes we have one two three four esses and then it looks like two peas and again if you add these together two plus four plus four plus one hey that equals eleven the total number of objects that's all this condition says it says well then there are in factorial over n sub 1 factorial times n sub 2 factorial up to n sub R factorial all being multiplied so as we get that many linear arrangements of the end given objects again objects of the same type are indistinguishable so it says the number of linear Arrangements in this case well all we do is we take the total number which is 11 factorial and then we just take our different types and we just take factorials of each of those so 1 factorial 4 factorial 4 factorial 2 factorial and now this is what we get to simplify down here I did not do not have a calculator let's see if we can't do this by hand so 11 factorial that's just 11 times 10 times 9 times 8 times 7 times 6 times 5 times 4 times 3 times 2 times 1 squeeze that in there 1 factorial is just 1 I'll stick it in there 4 factorial 4 times 3 times 2 times 1 another 4 times 3 times 2 times 1 from our other 4 factorial and then 2 factorial is just 2 times 1 usually I cancel out the largest factorials that I can so we can cancel out a 4 3 2 and a 1 with a 4 3 a 2 and a 1 in the numerator let's see we've got 4 times 2 4 times 2 would be 8 so we can cancel the 8 out in the numerator let's see 3 times 2 would be 6 so we can also cancel it looks like the 6 out of the numerator and I don't think is anything else cancelling I don't think so so to me it looks like we're left with 11 times 10 times 9 times 7 times 5 let's see here so 11 times 10 that would be 110 9 times 7 that's 63 and then times 5 I think we're almost there let's see 110 times 63 60 times 1/10 would be 6600 plus another I guess 3 10 so 110 and 63 that should give us 6 9 3 0 then we would have to multiply that by 5 let's see if you multiply 7,000 by 5 we would get I guess 35,000 but we've kind of overshot that by 70 each time and we've done that five times which would be 350 so 35,000 - 350 what would that be three four six five zero if the math in my head is right let me see let me type this in here real quick so six nine three zero times come on three four six five zero perfect all right so it looks like to me there's thirty four thousand six hundred and fifty different linear combinations of the word Mississippi so again nothing too crazy here just another formula to remember so I'm going to do another example involving linear arrangements at some point - we'll also talk about how you can go from linear Arrangements maybe to circular Arrangements so maybe you're kind of a you know assigning people seats or you know around a table or something uh you know men and women so we'll look at the different number of circular arrangements as well but another linear arrangement problem coming I hope this one makes some sense and helps you out