# Arranging Talent: Math Behind Performance Sequences

Chapter 4, Problem 6

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QUESTION:

Show Programs Three bands and two comics are performing for a student talent show. How many different programs (in terms of order) can be arranged? How many if the comics must perform between bands?

##### Arranging Talent: Math Behind Performance Sequences

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Explore the fascinating world of permutations to determine the number of possible arrangements for a talent show. Learn how constraints change the number of valid sequences and delve into combinatorial techniques.

QUESTION:

Show Programs Three bands and two comics are performing for a student talent show. How many different programs (in terms of order) can be arranged? How many if the comics must perform between bands?

Step 1 of 3

In the problem, we are asked to find two numbers:

1. number of possible orders of the 5 performers - 3 bands and 2 comics

2. number of orders of the performers such that comics come in between bands

To find these numbers, use the permutation rule and the counting rule.