Question
The library has 6 new books it would like to display near the checkout desk. The librarian plans to place the six books between a set of bookends. How many different ways can the books be placed between the bookends if order is important?
Answers
GPT-4o mini
To determine the number of different ways the 6 new books can be arranged between the bookends, we can recognize that this is a problem of counting permutations.
Since the order in which the books are placed is important, we need to calculate the number of permutations of 6 distinct books. The number of permutations of \( n \) distinct items is given by \( n! \), which is the factorial of \( n \).
For 6 books, the calculation is as follows:
\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1
\]
Calculating this step by step:
- \( 6 \times 5 = 30 \)
- \( 30 \times 4 = 120 \)
- \( 120 \times 3 = 360 \)
- \( 360 \times 2 = 720 \)
- \( 720 \times 1 = 720 \)
Thus, the total number of different ways to arrange the 6 books between the bookends is
\[
\boxed{720}
\]
Since the order in which the books are placed is important, we need to calculate the number of permutations of 6 distinct books. The number of permutations of \( n \) distinct items is given by \( n! \), which is the factorial of \( n \).
For 6 books, the calculation is as follows:
\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1
\]
Calculating this step by step:
- \( 6 \times 5 = 30 \)
- \( 30 \times 4 = 120 \)
- \( 120 \times 3 = 360 \)
- \( 360 \times 2 = 720 \)
- \( 720 \times 1 = 720 \)
Thus, the total number of different ways to arrange the 6 books between the bookends is
\[
\boxed{720}
\]