By counting principle rule, we have
[tex]\begin{gathered} \text{three men out of eight} \\ \binom{8}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{two women out of seven} \\ \binom{7}{2} \end{gathered}[/tex]Then the ways a committee of three men and two women can be formed is
[tex]\binom{8}{3}\cdot\binom{7}{2}=1176[/tex]Therefore, there are 1176 possible ways.
