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**heathrowjohnny** 1. A wine collection consists of $\displaystyle 4 $ bottles of cabernet and $\displaystyle 7 $ bottles of zinfandel. Randomly selecting $\displaystyle 6 $ bottles, find the following:

(a) $\displaystyle P \{\text{all cabernets are selected} \} = \frac{\binom{6}{4}}{\binom{11}{6}} $

(b) $\displaystyle P \{\text{at least 1 is a cabernet} \} = \frac{\binom{6}{1} + \binom{6}{2} + \binom{6}{3} + \binom{6}{4} + \binom{6}{5} + \binom{6}{6}}{\binom{11}{6}} $

Are these correct?