A gumball machine has six red gumballs,four blue gumballs,and three yellow gumballs.If you buy three gumballs,what is the probability that you get three different colors?

Question

Quizplus · Accepted Answer

The probability of getting three gumballs of different colors can be calculated by considering the total ways to pick one gumball of each color divided by the total ways to pick any three gumballs. The total ways to pick one gumball of each color is simply the product of the number of gumballs of each color, which is 6 (red) * 4 (blue) * 3 (yellow) = 72 ways. The total ways to pick any three gumballs from the 13 available (6 red + 4 blue + 3 yellow = 13) is calculated using combinations (since the order of selection does not matter), which is 13 choose 3 = 13! / (3!(13-3)!) = 286 ways. Therefore, the probability is 72 / 286 = 0.252.

A Gumball Machine Has Six Red Gumballs,four Blue Gumballs,and Three