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# Determining Amount of Group Combinations

A computer programming team has 12 members.

(a) How many ways can a group of 7 (out of the 12 members) be chosen to work on a special project? Explain.

(b) Suppose that out of the 12 members on the team 7 are IT majors and 5 are math majors.
(i) How many groups of 7 people can be formed that contain 4 IT majors and 3 math majors? Explain.
(ii) How many groups of seven can be formed that contain a least 1 IT major? Explain.
(c) Suppose that two team members (of the 12 of either major) refuse to work together. How many groups of seven can be chosen to work on a project? Explain.

(d) Suppose that two team members insist on either working together or not at all on projects. (That is, either the two people both work on the project together or neither will work on the project.) How many groups of seven can be chosen to work on a project? Explain.

#### Solution Preview

A computer programming team has 12 members.

(a) In how many ways can a group of 7 (out of the 12 members) be chosen to work on a special project? Explain.

Solution: We want to find all the possible combinations of 7 members, taken from the group of 12 members. Then using the combination formula, we obtain
(12)
(7) =12!/7!5!=792
So a group of 7 out of 12 members can be chosen in 792 ways.

(b) Suppose that out of the 12 members on the team 7 are IT majors and 5 are math majors.

(i) How many groups of 7 people can be formed that contain 4 IT majors and 3 math majors? Explain.

Solution: We want ...

#### Solution Summary

Combinations are clearly explained and the concepts applied in this tutorial.

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