Odds of getting specific color of Jelly Beans in a handful? I have a bag of jelly beans with approx 1190 Jelly Belly's in it. There are 50 different flavors. Assuming the amount of Jelly Belly's per flavor are equal (so, 23.8 of each bean):
If I pull 6 Jelly Beans from my unopened bag, what are the odds that 3 of them will be the same color?
I'm asking because I got a bag of jelly beans for Christmas and got 3 of the same color in the handful I just pulled out... and it's been many many years since my statistics class in college.
Thank you for the help. It's driving me batty and nobody at work cares about my Jelly Belly question except me =(
I would have tried to figure this out on my own as it seems very easy, but I don't even know where to begin looking.
 A: Let's pretend the bag is very large, so drawing one bean of a flavor doesn't change the probabilities.  There are $50^6$ possible draws, all the same probability.  The ways to get exactly $3$ of a flavor can be counted as $\binom 63=15$ choices for which $3$ will match times $50$ choices for which flavor to match times $49^3$ for the other $3$.  There is a tiny error as we double count the case you get two three of a kinds.  So the chance is $\frac {15*50*49^3}{50^6}=352947/62500000 = 0.005647152$ or about $1$ in $177$.  
A: It's called "probability without replacement".  The answer is (23.8/1190) x (22.8/1189) x (21.8/1188), so the probability of that happening is one in 142,094.
A: The accepted answer is incorrect (logic is right) but 6C3 = 20 (not 15) , hence the final answer would be .0077 not .0056
Also another way to look at this is plain old binomial probability : nCr p^r (1-p)^n-r 
Here we have 6 tries (n=6), to get 3 success (same color, r=3 ) , probability of  success won't change in any meaningful way as beans are too many (1190) . 
Calculating p (probability of success is bit tricky ) Its 24/1190 ( as 23.8 are of same color) . 
So for a one specific color 
Pr(x=3 same color) = 6C3*(24/1190)^3 (1166/1190)^3 = .000154. 
But this could be true for any of the 50 flavor possible , so 50*0.000154 = .0077

