Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

In how many different ways can five elements be selected in order from a set with five elements when repetition is allowed?

There are 3125 ways in which five elements can be selected in order from a set with five elements when repetition is allowed.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definitions

Definition of Permutation (Order is important)

No repetition allowed: $P (n, r) = \frac{n!}{(n - r)!}$

Repetition allowed: $n^{r}$

Definition of combination (order is important)

No repetition allowed: data-custom-editor="chemistry" $C (n, r) = (\begin{array}{l} n \\ r \end{array}) = \frac{n!}{r! (n - r)!}$

Repetition allowed: $C (n + r - 1, r) = (\begin{matrix} n + r - 1 \\ r \end{matrix}) = \frac{(n + r - 1)!}{r! (n - 1)!}$

with $n! = n (n - 1) \cdot . . . . . \cdot 2 \cdot 1$

Step 2: Solution

The order of the elements matters (since we want to select the elements in order), thus we need to use the definition of permutation.

We are interested in selecting r = 5 elements from a set with n = 5 elements.

Repetition of elements is allowed.

$n^{T} = 5^{5} = 3125$

Thus there are 3125 ways in which five elements can be selected in order from a set with five elements when repetition is allowed.

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Discrete Mathematics and its Applications

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Short Answer

In how many different ways can five elements be selected in order from a set with five elements when repetition is allowed?

Step by Step Solution

Step 1: Definitions

Step 2: Solution

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Discrete Mathematics and its Applications

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In how many different ways can five elements be selected in order from a set with five elements when repetition is allowed?

Step by Step Solution

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Step 2: Solution

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