■ Counting Principles Solve these exercises by using the appropriate counting principle(s).
Choosing a Committee A committee of six is to be chosen from a class of students. The committee is to consist of a chair, a secretary and four other members. In how many different ways can the committee be picked?
The number of different ways the committee of six members can be picked.
A committee of six is to be chosen from a class of students. The committee consists of a chair, a secretary and four other members.
The order for picking a student for the post of a chair, a secretary, and four other members is important, But the order for picking the four other members is not important.
Write the formula of the number of permutations,
Here, is the total number of objects and is the number of objects chosen.
Write the formula of the number of combinations,
Substitute for and for in equation as.
Substitute for and for in equation
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