Question 548259
If there are AT LEAST three men on the committee, this means there could be 4 or 5 men.  We will look at each case. 

If there are 3 Men and 2 Women. 
There are {{{(7C3)}}} ways to pick the 3 men (note it is a combination as order does not matter).  
There are {{{(6C2)}}} ways to pick the 2 women (again, order doesn't matter)
These two things are done at the same time, so we can use the product rule. 
{{{(7C3)(6C2)}}}


If there are 4 men and 1 woman
There are {{{(7C4)}}} ways to pick the 4 men (note it is a combination as order does not matter).  
There are {{{(6C1)}}} ways to pick the 1 woman (again, order doesn't matter)
These two things are done at the same time, so we can use the product rule. 
{{{(7C4)(6C1)}}}

If it is all men 
There are {{{(7C5)}}} ways to pick the 5 men.



Now, we can add all these three options up and get our final answer.  I will let you do this.  
If you are unsure of answer please feel free to let me know:)