Short Probability (permutation) question

In summary, the conversation discusses the number of possible seating arrangements for a semi-circle of 19 students, where 4 of the students must sit next to each other. The question is whether the calculation is 15! x 4! or 19! / 4!, with the first option being the preferred choice.
  • #1
jasper10
55
0

Homework Statement



There is a total of 19 students sitting in a semi-cirlce. How many seating arrangements are possible, if 4 of the 19 students have to sit next to each other?


The Attempt at a Solution



I'm not sure if the calculation is:

15! x 4!

or

19! / 4!

Thanks!
 
Physics news on Phys.org
  • #2
jasper10 said:

Homework Statement



There is a total of 19 students sitting in a semi-cirlce. How many seating arrangements are possible, if 4 of the 19 students have to sit next to each other?


The Attempt at a Solution



I'm not sure if the calculation is:

15! x 4!

or

19! / 4!

Thanks!

I would go with the first answer, assuming you can explain it. :smile:
 

What is a permutation?

A permutation is an arrangement of a set of objects in a specific order. It is often used to calculate the number of possible outcomes in a given scenario.

What is the formula for calculating permutations?

The formula for calculating permutations is nPr = n! / (n-r)!, where n represents the total number of objects and r represents the number of objects being chosen for the arrangement.

What is the difference between a permutation and a combination?

A permutation involves arranging a set of objects in a specific order, while a combination involves selecting a subset of objects from a larger set without regards to order.

When is it appropriate to use a permutation?

A permutation is appropriate when the order of objects matters in the scenario. For example, when calculating the number of possible outcomes of a race or the number of ways to arrange books on a shelf.

What are some real-world applications of permutations?

Permutations are commonly used in fields such as statistics, genetics, and cryptography. They can also be applied in various scenarios such as lottery drawings, password combinations, and scheduling activities.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
2
Views
847
  • Precalculus Mathematics Homework Help
Replies
12
Views
1K
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
9
Views
968
  • Precalculus Mathematics Homework Help
Replies
16
Views
2K
  • Precalculus Mathematics Homework Help
Replies
8
Views
401
  • Precalculus Mathematics Homework Help
Replies
29
Views
2K
  • Precalculus Mathematics Homework Help
Replies
20
Views
3K
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
4
Views
2K
Back
Top