IEE 380 Ch 2 Combinations Addition Rule Independence

well this slide some of you are probably familiar with if you've taken discrete math maybe even if you haven't but this is something called a combination and it's also something called the binomial coefficient so you know what is combination maybe but it's also called as I said the binomial coefficient and we're going to see this uh coming up

very shortly so a combination uh sometimes looks like this it's a c with n in the upper like the superscript and then subscript is in R the notation is n over R in parentheses and this is what it looks like mathematically when we see it like this we're like this we would say typically we would say n

choose R so what is this it's when we're taking from our items I'm sorry we take our items from a set of n or circumstances or whatever where and the key word here is order doesn't matter so for example if my sample space uh existed uh I mean these could even be I guess grades I suppose a

b c and d then we have four possibilities here and then I'm going to take if I wanted to take a selection of just four for example there's only one combination a b c d but order doesn't matter so that would be the same as same as like um D C B A or B a c d or and you could

keep going so there's just one combination the order doesn't matter if R is two there would be there would be six combinations so we would have a b a c a d b c b d and c d where a b would be the same as B A and A C would be the same as C A and

you get the ideas the order does not um matter here at all and we can count them and so that would be six so for example n choose R when n is 4 and R is one we can see that that's just one but mathematically that would be 4 factorial over one factorial and then four minus