Question 970100
One specific woman must be selected.

Now we are choosing from 4 men and 5 women and the committee size is effectively 6

Choose all 4 men (1 way).  Choose 2 women from 5  5 C2  (10 ways); Sub-total= product or 10 ways
Chose 3 men out of 4 (4 ways). Choose 3 women out of 5  (10 ways); sub-total= product or 40 ways.
Chose 2 men out of 4 (6 ways). Choose 4 women out of 5 (5 ways); sub-total= product or 30 ways.
Choose 1 man out of 4 (4 ways). Choose all 5 women (1 way)  4 ways

That would be 10 +40+30 +4= 84 ways