**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**

It is given that The total number of cards = 8

Answered: In how many different orders can you…

Math

Statistics

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...

See similar textbooks

Similar questions

In horse racing, a “trifecta” occurs when a bettor wins by selecting the first three finishers in the exact order (1 St place, 2nd place, and 3rd place). How many different trifectas are possible if there are 14 horses in a race?
In three-card poker, a hand consists of three cards dealt from a deck of 52. How many different three-card poker hands are possible? (Order is not important.)
A coffee shop has 7 Guatemalan roasts, 4 Cuban roasts, and 10 Costa Rican roasts. How many ways can the shop choose 2 Guatemalan, 2 Cuban, and 3 Costa Rican roasts for a coffee tasting event?
How many different ways can 6 people be seated at a round table.
In how many ways can 10 teenagers be seated at a round table if 2 girls wish to sit with their boyfriends.
DISCUSS: Complementary Combinations Without performing any calculations, explain in words Why the number of ways of choosing two objects from ten objects is the same as the number of ways of choosing eight Objects from ten objects. In explain Why c(n,r)=c(n,nr)
How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?
A motorcycle shop has 10 choppers, 6 bobbers, and 5 café racers—different types of vintage motorcycles. How many ways can the shop choose 3 choppers, 5 bobbers, and 2 café racers for a weekend showcase?
a In solving a problem involving picking r objects from n objects, how do you know whether to use permutations or combinations? b Would you use combinations or permutations in counting the following: i The number of five-card hands from a 52-card deck. ii The number of ways in which first, second, and third prizes can be awarded in a ten-person race.
Over the past year, John has purchased 30 books. a In how many ways can he pick four of these books and arrange them, in order, on his nightstand bookshelf? b In how many ways can he choose four of these books to take with him on his vacation at the shore?
An art store has 4 brands of paint pens in 12 different colors and 3 types of ink. How many paint pens are there to choose from?
Choosing Officers From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer need to be filled. In how many different ways can the offices be filled?