Question
A bookshelf has 8 different books. How many different ways can these 8 books be arranged on the shelf?
Is this a combination or a permutation? (2 points)
Combination
How many different ways can the books be arranged? (5 points)
Is this a combination or a permutation? (2 points)
Combination
How many different ways can the books be arranged? (5 points)
Answers
GPT-4o mini
The arrangement of books is a permutation because the order of the books matters.
To find the number of different ways to arrange 8 different books, we use the formula for permutations of \( n \) distinct objects, which is given by \( n! \) (n factorial).
For 8 different books, the number of arrangements is:
\[
8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320.
\]
Therefore, the number of different ways the 8 books can be arranged on the shelf is **40,320**.
To find the number of different ways to arrange 8 different books, we use the formula for permutations of \( n \) distinct objects, which is given by \( n! \) (n factorial).
For 8 different books, the number of arrangements is:
\[
8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320.
\]
Therefore, the number of different ways the 8 books can be arranged on the shelf is **40,320**.