A membership committee of three is formed from four eligible members. Let the eligible members be represented by cap A , cap b , cap c , and cap d The possible outcomes include cap s is equal to ABC, ABD, ACD, BCD . Which statements about the situation are true? Choose three correct answers.
Answer
A
There are three ways to form the committee if person cap d must be on it.
B
If persons cap b and cap c must be on the committee, there are two ways to form the committee.
C
There are four ways to choose the committee.
D
If persons cap A and cap c must be on the committee, then there is only one way to form the committee.
E
If seven members are eligible next year, then there will be fewer combinations.
Explanation
A three-person committee from four members can be formed in four ways: ABC, ABD, ACD, and BCD, so A is true. If D must serve, the other two members can be chosen from A, B, and C in three ways, so D is true. If B and C must serve, the third member can be either A or D, giving two ways, so E is true.
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