Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 12.2
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Exercise 58 Page 670

We have n factorial (n!) ways to arrange n different things in a sequence.

1440 ways

Practice makes perfect
We want to arrange 5 different French books and 3 different Spanish books on a shelf, making sure that all books of the same language remain together. Within each such arrangement we either have Spanish books before the French ones, or the French ones before the Spanish ones. SpanishFrench or FrenchSpanish Now, recall that n factorial (n!) gives us the number of ways to arrange n different things in a sequence. Let's use this fact to find how many ways we have to arrange the books in each language. 5French books ⇒ 5! ways to arrange them 3Spanish books ⇒ 3! ways to arrange them We have 2 ways to order the languages, 5! ways to order the French books and 3! ways to order the Spanish books. Since each ordering is independent of the others, the total number of ways in which we can order the books is the product of these numbers. 2 * 5! * 3! Finally, let's find the value of this expression.
2 * 5! * 3!

Write as a product

2 * (5 * 4 * 3 * 2 * 1) * (3 * 2 * 1)
1440