jmc

In this problem, we're really selecting two separate committees. We can choose 3 men from the 30 men total in $$\left(\genfrac{}{}{0ex}{}{30}{3}\right)=\frac{30\times 29\times 28}{3\times 2\times 1}=4,060$$ways, and 4 women from the 40 women total in $$\left(\genfrac{}{}{0ex}{}{40}{4}\right)=\frac{40\times 39\times 38\times 37}{4\times 3\times 2\times 1}=91,390$$ways. Since these two selections are independent (since for each of the $4,060$ ways to pick the men, there are $91,390$ ways to pick the women), we multiply them together to get the number of ways that we can form the 7-member overall committee: $$\left(\genfrac{}{}{0ex}{}{30}{3}\right)\left(\genfrac{}{}{0ex}{}{40}{4}\right)=(4,060)(91,390)=\boxed{371,043,400}.$$