A computer programming section has 11 members. A team of 5 is to be chosen to work on a special project. (a) How many ways can the team be chosen?  (b) Suppose there are 6 men and 5 women in the section.       How many teams of 5 have no women?       How many teams of 5 have one woman ?      How many teams of 5 have two women?      How many teams of 5 have at most two women?  (c) Two team members refuse to work together on projects. The teams must include one or neither of them. Now how many teams of 5 can be chosen to work on the project?

Advanced Engineering Mathematics
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ISBN:9780470458365
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A computer programming section has 11 members. A team of 5 is to be chosen to work on a special project.

(a) How many ways can the team be chosen? 

(b) Suppose there are 6 men and 5 women in the section.

      How many teams of 5 have no women? 

     How many teams of 5 have one woman ? 

    How many teams of 5 have two women? 

    How many teams of 5 have at most two women? 

(c) Two team members refuse to work together on projects. The teams must include one or neither of them. Now how many teams of 5 can be chosen to work on the project? 

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