major probability

$\text{a) $p = \dfrac{\dbinom{12}{3}\dbinom{16}{2}\dbinom{18}{2}}{\dbinom{46}{7}}$}$

$\text{b) $P[\text{at least 2 red balls withdrawn}] = 1 - P[\text{0 or 1 red balls withdrawn}]$}=\\ 1 - \dfrac{\dbinom{12}{0}\dbinom{34}{7}}{\dbinom{46}{7}} - \dfrac{\dbinom{12}{1}\dbinom{34}{6}}{\dbinom{46}{7}}$

$\text{c) $P[\text{all balls the same color}]$}=\\ \dfrac{\dbinom{12}{7}+\dbinom{16}{7}+\dbinom{18}{7}}{\dbinom{46}{7}}$

$\text{d) $P[\text{3 red or 3 blue withdrawn}]$}=\\ \dfrac{\dbinom{12}{3}\dbinom{34}{4} + \dbinom{16}{3}\dbinom{30}{4}}{\dbinom{46}{7}}$