Yes. You can do the complement method as you described @notak. It is 1 - Prob(4 men, no women selected) or 1 - Prob(Less than 1 woman in committee).

The complement method (1 minus way) is nice so you do not have to add all the cases where you have 1W3M, 2W2M and 3W1M. This complement method works with any probability distribution (discrete or continuous with integrals). Not just binomial.