There are three cases that we can solve.
CASE 1:
Committee with 6 women (no men)
Choose the 6 women --> C (17,6)
= (17 x 16 x 15 x 14 x 13 x 12) / (6 x 5 x 4 x 3 x 2 x 1)
= 12,376 ways
CASE 2:
Committee with 5 women and 1 man
Choose the 5 women --> C(17,5)
= 6,188 ways
Choose the 1 man --> C(8,1)
= 8 ways
Multiply:
C(17,5) * C(8,1)
=6,188 x 8
= 49,504 ways
CASE 3:
Committee with 4 women and 2 men:
Choose the 4 women --> C(17,4)
= 2,380 ways
Choose the 2 men --> C(8,2)
= 28 ways
Multiply:
C(17,4) * C(8,2)
=2,380 x 28
= 66,640 ways
There aren't any other valid cases (e.g. 3W+3M, 2W+4M, 1W+5M, 6M) so you are done.
Add up all the valid cases:
12,376 + 49,504 + 66,640 = 128,520 ways
Answer:
There are 128,520 ways to form a committee of 6 members (where there are strictly more women than men)
