Explanation 1) Definition: The Fundamental Counting Principle, If we want to perform a series of tasks and the first task can be done in a ways, the second can be done in b ways, the third can be done in c ways, and so on. Then all the tasks can be done in a × b × c × ... ways. 2) Calculation: Given, The students in the 12-member advanced communications design class at center city community college are submitting a project to a national competition. Stage 1: Select a two members for a team leader and a main presenter from 12-member. (i.e.) P ( 12 , 2 ) Stage 2: Then, select the remaining two members of four-member team from the remaining member after selecting team leader and main presenter. (i.e.) C ( 10 , 2 ) This, we can apply the fundamental counting principle. Stage 1: P ( 12 , 2 ) Using the formula for permutation, P ( n , r ) = n ! ( n − r ) ! Here n = 12 and r = 2 P ( 12 , 2 ) = 12 ! ( 12 − 2 ) ! P ( 12 , 2 ) = 12 ! 10 ! P ( 12 , 2 ) = 12 ⋅ 11 ⋅ 10 ! 10 ! P ( 12 , 2 ) = 12

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Chapter 12.3, Problem 63E

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The number of ways can this team be formed.

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Chapter 12.3, Problem 62E

Chapter 12.3, Problem 64E

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The number of ways can this team be formed.

Solution Summary: The author explains the Fundamental Counting Principle and how it can be applied to a 12-member advanced communications design class.

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To find:

The number of ways can this team be formed.