SOLUTION: How many ways can you select a committee of 7 from 4 males and 6 females if a certain woman must be in the committee?

Question 970100: How many ways can you select a committee of 7 from 4 males and 6 females if a certain woman must be in the
committee?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
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

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