AP EAMCET Engineering 2012 Solved Paper

A committee of 12 members is to be formed when women are in majority.
Case I 9 women and 3 men :
∴ Number of ways =‌9C9×‌8C3=1×

8×7×6

3×2×1

=56
Case II 8 women and 4 men
∴ Number of ways =‌9C8×‌8C4
=9×

8×7×6×5

4×3×2×1

=630
Case III 7 women and 5 men
∴ Number of ways =‌9C7×‌8C5
=

9×8

2×1

×

8×7×6

3×2×1

=36×56=2016
∴ Required number of ways =56+630+2016
=2702