A Committee of 4 in which at least 2 women are there.

Out of 10 men, Teachers = 5

Doctors = 3 and Business man = 2

Out of 8 women, Teachers = 3 and Doctors = 2

Researchers = 2 and Social worker = 1

Number of ways of selecting 4 members in which at least 2 are women

= (2 men , 2 women) + (1 men , 3 women) + (0 men , 4 women)

= $$(C^{10}_2 \times C^8_2) + (C^{10}_1 \times C^8_3) + (C^{10}_0 \times C^8_4)$$

= $$(\frac{10 \times 9}{1 \times 2} \times \frac{8 \times 7}{1 \times 2}) + (\frac{10}{1} \times \frac{8 \times 7 \times 6}{1 \times 2 \times 3}) + (\frac{8 \times 7 \times 6 \times 5}{1 \times 2 \times 3 \times 4})$$

= $$(45 \times 28) + (10 \times 56) + (70)$$

= $$1260 + 560 + 70 = 1890$$