A box is filled with 15 different socks: 10 green and 5 yellow. Three socks are picked from the box (leaving 12 in the box). Let $x$ be the random variable describing the number of green socks that are selected. Let events $A$ and $B$ be described as follows:
$A$ = the event that not all three socks are green.
$B$ = the event where the first sock selected is green.
Find $P(A)$, $P(B)$, and $P(A\text{ and }B)$. Show any appropriate $nCr $ expressions.
I know for this problem that $P(A) = 1 - (\frac{10}{15} \times \frac{9}{14} \times \frac{8}{13})$ and $P(B) = \frac{10}{15}$, but I'm not sure how to find $P(A\text{ and }B)$. I know these events are dependent.