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A total of 2 freshmen, 3 sophomores, 4 juniors and 5 seniors have been nominated to

Chapter 8, Problem 8

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QUESTION:

A total of 2 freshmen, 3 sophomores, 4 juniors and 5 seniors have been nominated to serve on a committee. How many different committees are possible if: (a) the committee can consist of any 4 students? (b) the committee must consist of one student from each class? (c) the committee is to consist of 3 students from 3 different classes?

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QUESTION:

A total of 2 freshmen, 3 sophomores, 4 juniors and 5 seniors have been nominated to serve on a committee. How many different committees are possible if: (a) the committee can consist of any 4 students? (b) the committee must consist of one student from each class? (c) the committee is to consist of 3 students from 3 different classes?

ANSWER:

Step 1 of 4

Combination

Let be an -element set. An -element subsets of , where is called an

combination of .

Therefore, the number of -combination of an -element set is

An -combination is also referred to as an unordered list of -elements or as an -selection.

Objective of the question is how many different committees are possible if the committee can

consist of any 4 students

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