ChrisS
  • ChrisS
A committee of five people is to be chosen from a club that boasts a membership of 10 men and 12 women. How many ways can the committee be formed if it is to contain at least two women? How many ways if, in addition, one particular man and one particular woman who are members of the club refuse to serve together on the committee?
Mathematics
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ChrisS
  • ChrisS
A committee of five people is to be chosen from a club that boasts a membership of 10 men and 12 women. How many ways can the committee be formed if it is to contain at least two women? How many ways if, in addition, one particular man and one particular woman who are members of the club refuse to serve together on the committee?
Mathematics
schrodinger
  • schrodinger
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
(12C2)*(20C3) for the first one
anonymous
  • anonymous
(12C2)*(20C3)-(2C2)*(11C1)(19C2) for the second question
ChrisS
  • ChrisS
To get the total combinations without restriction of any kind, I would use (22C5) right? If that is the case I don't see the first answer because that gives me a number larger than the total without restriction. (22C5)=22,334 (12C2)*(20C3)=75240

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ChrisS
  • ChrisS
@Luis, how did you arrive at your answers?
anonymous
  • anonymous
oops the * are suppose to be + , its been a whilte since I did this type of questions
anonymous
  • anonymous
(12C2)+(20C3) (12C2)+(20C3)-(2C2)+(11C1)+(19C2)
ChrisS
  • ChrisS
Thank you!
anonymous
  • anonymous
the second should really be (12C2)+(20C3)-[(2C2)+(11C1)+(19C2)] sorry, i'm missing brackets

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