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
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 47SE: How many ways can a baseball coach arrange the order of 9 batters if there are 15 players on the...
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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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