Choosing Vertices of a Polygon from Random Points on a Circle: How Many Ways?

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In summary, the formula for calculating the number of ways is n!/(n-r)!, where n is the total number of items and r is the number of items we are choosing. The "n choose r" formula is used to calculate the number of ways to choose a specific number of items from a larger set, known as a combination. The main difference between permutations and combinations is that permutations consider order while combinations do not. The "n choose r" formula is only applicable in certain scenarios, such as choosing a specific number of items from a larger set. In real life, it can be used in various situations such as forming a committee, choosing items from a menu, and in probability calculations.
  • #1
physicsss
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"Number of ways" question

A circle has random points on its circumferance. How many ways can you form a quadrilateral, a triangle, and a octagon using these points?

I have no idea how to get an numerical answers for this question without using n to represent the number of points on the circle.

Thanks.
 
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  • #2
I think using 'n' is fine...just make a correct formula such that for any n you can get a specific answer.
 
  • #3
Of course you need n.
In how many ways can you choose the vertices of an r sided polygon from n points ?
 

1. What is the formula for calculating the number of ways?

The formula for calculating the number of ways is n!/(n-r)!, where n is the total number of items and r is the number of items we are choosing.

2. How do I know when to use the "n choose r" formula?

The "n choose r" formula is used when we need to calculate the number of ways to choose a specific number of items from a larger set. This is also known as a combination, where order does not matter.

3. What is the difference between permutations and combinations?

Permutations are arrangements where the order of items matters, while combinations are selections where order does not matter. For example, choosing three colors from a set of five would result in a combination, while arranging three letters from the alphabet would result in a permutation.

4. Can the "n choose r" formula be applied to any scenario?

No, the "n choose r" formula is only applicable when we are choosing a specific number of items from a larger set. If the scenario involves selecting items with certain restrictions or conditions, a different formula may need to be used.

5. How can I use the "n choose r" formula in real life situations?

The "n choose r" formula can be useful in various real life situations, such as calculating the number of ways to form a committee or choosing a combination of items from a menu. It can also be used in probability calculations, such as finding the chances of getting a certain hand in a card game.

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