If there are more women than men, then there are either 3 women, 1 man or there are 4 women, 0 men.
If there are 3 women, 1 man, then there are a total of $\dbinom{5}{3} \times \dbinom{15}{1} = 150$ ways of doing it.
If there are 4 women, 0 men, then there are a total of $\dbinom{5}{4} \times \dbinom{15}{0} = 5$ ways of doing it.
Therefore, there are a total of $\boxed{155}$ ways of doing it.