Question

The Fundamental Counting Principle can be used to determine the number of ways of arranging the numbers 1, 2, 3, 4, 5,..., 98, 99, 100.
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Part 1
Choose the correct answer below.
A.
This statement does not make sense because the Fundamental Counting Principle is only used to find the number of ways in which a series of successive things can occur.
B.
This statement makes sense because the Fundamental Counting Principle is used to find the number of ways in which one thing can occur.
C.
This statement makes sense because the Fundamental Counting Principle is used to find the number of ways in which a series of successive things can occur.
D.
This statement does not make sense because the Fundamental Counting Principle is only used to find the number of ways in which one thing can occur.

Answer 1

C.

Reason: Arranging the 100 numbers is a sequence of 100 successive choices: 100 choices for the first position, 99 for the second, ..., 1 for the last. By the Fundamental Counting Principle the total number is 100·99·...·1 = 100!.