A committee has 25 members;15 whom are women and 10 men.
-How many ways can a subcommittee of 8 be chosen to work on a project if
*anyone of the committee be chosen?
(25 members, Choose 8) = 25C8 = 1081575

*at most 2 women can be chosen?

Three cases:

Case 1.  Choose no women at all.  (That's all men)

(10 men members, Choose 8) = 10C8 = 45

Case 2.  Choose 1 woman and 7 men. 

(15 women, Choose 1)*(10 men, Choose 7) = 15C1*10C7 = 15*120 = 1800

Case 3.  Choose 2 woman and 6 men. 

(15 women, Choose 2)*(10 men, Choose 6) = 15C2*10C6 = 105*210 = 22050

Grand total:  45 + 1800 + 22050 = 23895

Edwin
  

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