We must choose at least 3 women, so we calculate the case of 3 women, 4 women and 5 women and by addition rule add the result.
12C3 x 20C2 +12C4 x 20C1 + 12C5 x 20C0 = (12x11x10/3x2x1) x (20x19/2x1) + (12x11x10x9/4x3x2x1) x 20 + (12x11x10x9x8/5x4x3x2x1) x 1
= 220 x 190 + 495 x 20 + 792
= 52492