A computer programming team has 13 members.
a. How many ways can a group of seven be chosen to work on a project?
b. Suppose seven team members are women and six are men.
(i) How many groups of seven can be chosen that contain four women and three men?
(ii) How many groups of seven can be chosen that contain at least one man?
(iii) How many groups of seven an be chosen that contain at most three women?
c. Suppose two team members refuse to work together on projects. How many groups of seven can be chosen to work on a project?
d. Suppose two team members insist on either working together or not at all on projects. How many groups of seven can be chosen to work on a project?
The number of groups of that can be chosen from members.
There are members in the team and only members should be chosen.
The number of combinations that can be chosen from a set of elements is given by .
When selecting the combinations of groups, the order is not considered. Also, no repetitions in the groups. Hence, we can substitute and into the formula
The number of groups of that satisfies following conditions.
The number of different groups of seven members without two specific team members together.
The number of groups of members with either both two members are together or both are not together.
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