The number of ways of choosing a committee of 4 out of 18 people is 18×17×16×15/4!=3060.
Of these there will be committees of 4 men and committees of 4 women. These must be excluded, leaving committees consisting of at least one man and one woman.
To exclude the all men committee we must remove all combinations of 4 men chosen from 8=8×7×6×5/4!=70. To exclude the all women committee we must remove all combinations of 4 women chosen from 10=10×9×8×7/4!=210. So if we exclude all men and all women committees we get:
3060-(70+210)=2,780 committees including at least one man and one woman.