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Q1E

Expert-verifiedFound in: Page 432

Book edition
7th

Author(s)
Kenneth H. Rosen

Pages
808 pages

ISBN
9780073383095

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

There are 243 ways in which five elements can be selected in order from a set with three elements when repetition is allowed.

**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: $C(n,r)=\left(\begin{array}{l}n\\ r\end{array}\right)=\frac{n!}{r!(n-r)!}$

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

with** data-custom-editor="chemistry" $\mathrm{n}!=\mathrm{n}(\mathrm{n}-1)\cdot .....\cdot 2\cdot 1$**

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 = 3 elements.

Repetition of elements is allowed.

${n}^{r}={3}^{5}=243$

Thus there are 243 ways in which five elements can be selected in order from a set with three elements when repetition is allowed.

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