Answer :
In order to find the probability you must start by finding the total possible outcomes for selecting a committee of six people from the 12 people.
[tex]\begin{gathered} 12C6=\frac{12!}{6!(12-6)!} \\ 12C6=\frac{12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{6\cdot5\cdot4\cdot3\cdot2\cdot1\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ 12C6=\frac{12\cdot11\cdot10\cdot9\cdot8\cdot7}{6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ 12C6=924 \end{gathered}[/tex]then find the possible ways of finding selecting a committee of 3 republicans and 3 democrats
[tex]\begin{gathered} 5C3\cdot7C3=\frac{5!}{3!(5-3)!}\cdot\frac{7!}{3!(7-3)!} \\ 5C3\cdot7C3=\frac{5!}{3!2!}\cdot\frac{7!}{3!4!} \\ 5C3\cdot7C3=10\cdot35 \\ 5C3\cdot7C3=350 \end{gathered}[/tex]Then we divide the possible outcomes with the total outcomes to find the probability
[tex]\begin{gathered} p=\frac{350}{924} \\ p=\frac{25}{66} \end{gathered}[/tex]the probability is equal to 25/66