If the majority are women implies that:
= (43)×(62)+(44)×(61)\binom{4}{3} \times \binom{6}{2} + \binom{4}{4} \times \binom{6}{1}(34)×(26)+(44)×(16)
= 4×15+1×64 \times 15 + 1 \times 64×15+1×6
= 60 + 6 = 66
