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A total of 2 freshmen, 3 sophomores, 4 juniors and 5 seniors have been nominated to
Chapter 8, Problem 8(choose chapter or problem)
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?
Questions & Answers
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