Red, blue, yellow, and green marbles are in a bag, with 14 marbles of each color. One white marble is added to the bag for a total of 57 marbles. If three marbles are chosen without replacement, what is the probability that all three marbles will be blue?

Since you have 57 marbles, wouldn't you just do 57*56*55? and then your answer would be 1/(57*56*55). Right?

Question

Red, blue, yellow, and green marbles are in a bag, with 14 marbles of each color. One white marble is added to the bag for a total of 57 marbles. If three marbles are chosen without replacement, what is the probability that all three marbles will be blue?

Since you have 57 marbles, wouldn't you just do 57*56*55? and then your answer would be 1/(57*56*55). Right?

phi · Answer

there are 14 blue out of 57  so on the first pick 
it is 14/57 chance of being blue
if you get a blue on that pick there are 13 out of 56  or 13/56 of getting another blue
and the chance for getting the third is 12/55
so (14*13*12)/(57*56*55)