**How many ways you can draw 3 balls in a box of 5 balls, if we replace the ball in box after being drawn?**- **n** - **r**- **Permutation Notation**- **Counting Principle**- **Answer**

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How many ways you can draw 3 balls in a box of 5 balls, if we replace the ball in box after being drawn? Counting Principle Permutation Notation Answer

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**How many ways you can draw 3 balls in a box of 5 balls, if we replace the ball in box after being drawn?**

- **n**

- **r**

- **Permutation Notation**

- **Counting Principle**

- **Answer**

Expert Solution

Step 1

Permutation: It means number of arrangements be obtained

It is denoted by $P (n, r) o r {}^{n}P_{r}$ where n is number of items and r is number are items to be arranged

The formula is given by

${}^{n}P_{r} = \frac{n!}{r! (n - r)!}$

If the items is to be drawn with replacement then number of ways to choose r items out of n items $n^{r}$

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