In how many different orders can you line up 8 cards on a table? a 8 Ob 1 Ос d 1,680 40,320
In how many different orders can you line up 8 cards on a table? a 8 Ob 1 Ос d 1,680 40,320
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CR: Chapter Review
Problem 4CC: a In solving a problem involving picking r objects from n objects, how do you know whether to use...
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![**Question:**
In how many different orders can you line up 8 cards on a table?
**Options:**
a) 8
b) 1
c) 1,680
d) 40,320
**Explanation:**
To determine the number of different ways to arrange 8 cards, you need to use the concept of permutations. The formula for the number of permutations of n distinct items is given by \( n! \) (n factorial).
For 8 cards, the calculation would be:
\[ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320 \]
Therefore, the correct answer is:
**d) 40,320**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b8f79a9-b6a4-48ca-ab39-5a4f4172185c%2Feb889fbe-3071-4144-9ba2-7ddfb1cd21c1%2Fsnvpwft_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
In how many different orders can you line up 8 cards on a table?
**Options:**
a) 8
b) 1
c) 1,680
d) 40,320
**Explanation:**
To determine the number of different ways to arrange 8 cards, you need to use the concept of permutations. The formula for the number of permutations of n distinct items is given by \( n! \) (n factorial).
For 8 cards, the calculation would be:
\[ 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320 \]
Therefore, the correct answer is:
**d) 40,320**
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