Question 647499: What is the value of c(9,3)? I cannot figure it out so I need help please. Thank you
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! I assume you mean (9 choose 3). By definition c(n,r) or (n choose r) is 
This sounds intimidating I know, but if you think about it, it isn't terrible.
Recall that a permutation is  , because for instance if we want to figure out the number of ways between 9 horses there can be a trifecta, then you would start with 9 horses to choose from, then 8, and then 7. Another way to think about this is you have  since you are eliminating the other 6 horses each time. Order matters in this case. For combinations, order doesn't matter. So, we factor out the order. Let's say you win if any of the three horses you pick takes win,place,and show. Well if you win, between horse A,B,C you could have win,place,show; w,s,p; s,w,p ... etc. There are 3! ways to do this. So let's divide it out. So we get  = C(9,3).
So this is  =  =  =  =  = 84.
C(9,3) = 84
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