Probability of picking balls without replacement

probability

The total number of (equally likely) outcomes is $14 \choose 4$ For a outcome to be favorable, you need to get 2 red balls out of 5, 1 blue out of 4, 1 green out of 3 and 0 yellow out of 2, so the total number of favorable outcomes is: ${5\choose 2}{4\choose 1}{3\choose 1}{2\choose 0}$ So the probability you are looking for is:

$$\frac{{5\choose 2}{4\choose 1}{3\choose 1}{2\choose 0}}{14 \choose 4}$$

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