An urn contains 5 red, 6 green, and 2 yellow balls.

Four balls are sampled without replacement. FInd the probability that

(1) there are more red balls than yellow balls in the sample

(2) at least one color appears at least twice

(3) the variance of the number of colors represented in the sample

(4) there are no red balls in the sample

(5) the conditional probability that all balls chosen are red, given that no yellow balls appear in the sample.