Whenever you see the language of "at least" in a combinatorics or probability, start by considering the ways that that particular outcome won't happen. As sanju mentioned, there is only one way to pick a committee with no women on it: the committee of 3 men and 2 children. (And we'll ignore for the moment that children make terrible committee members!).
So, we simply want to solve for the total number of possible committees, then subtract out that 1 instance that doesn't work.
A quicker way to solve for the total number of possible committees is by using factorials. If we want to choose 5 people out of 10, we can divide the factorial of the total pool of people by the factorial of the people we choose times the factorial of the people we don't. In other words:
10!/(5!*5!)
This simplifies to (10*9*8*7*6)/(5*4*3*2), which simplifies further to 2*9*2*7 = 252
252 - 1 = 251
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
