Chapter 8.5, Problem 85E

To determine

To find: whether the given statement is true or false.

Answer to Problem 85E

Given statement is True.

Explanation of Solution

Given information: Given statement is “The number of permutations of n elements can

be derived by using the Fundamental Counting Principle”.

Formula used:

Consider the following formula for permutation,

  ${}_n{P}_r=\frac{n!}{(n-r)!}$ .

Calculation:

Consider the following formula for permutation,

  ${}_n{P}_r=\frac{n!}{(n-r)!}$ .

And the fundamental counting principle is, if there are 2 persons and they can go by 3 cars, then the number of ways that the persons can drive is 2.3=6 ways.

Consider the statement that permutations of n elements can be derived by using the fundamental counting principle is True as both of them find number of ways of selection of different number of elements.