The maximum number of points of intersection of $8$ circles is
Show Hint
Use the formula of Permutation
- $16$
- $24$
- $28$
- $56$
The Correct Option is D
Approach Solution - 1
The correct answer is Option D) \(56\)
The maximum number of points of intersection = \(P^8_2=8 \times 7 = 56\)
Discover More from Chapter: Permutations and Combinations
Approach Solution -2
The correct answer is Option D) \(56\)
Real Life Applications
Some real-life examples of the maximum number of points of intersection of circles are
1. In computer graphics: To calculate the visibility of the objects in a computer graphics scene.
2. In physics: To calculate the interference patterns of waves
3. In mathematics: To study the topology of the plane.
Question can also be asked as
1. How many points of intersection can 8 circles have?
2. What is the maximum number of intersection points for 8 circles?
3. How can you calculate the maximum number of intersection points for 8 circles?
4. What is the Erdos–Szekeres theorem?
Approach Solution -3
The correct answer is Option D) \(56\)
Permutations and combinations are mathematical concepts used to count and calculate the number of possible arrangements or selections of objects.
Permutations
A permutation is an arrangement of objects in a specific order. The number of permutations of a set of objects is given by the formula:
P(n, r) = n! / (n - r)!
Where:
- n is the total number of objects in the set.
- r is the number of objects selected or arranged.
- "!" denotes the factorial operation, which is the product of all positive integers less than or equal to a given number.
Combinations
A combination is a selection of objects from a set without considering the order of the selection. The number of combinations of a set of objects is given by the formula:
C(n, r) = n! / (r!(n - r)!)
Where the variables n and r have the same meaning as in permutations.
Top Questions on permutations and combinations
- The number of four digit even numbers that can be formed using the digits 0, 1, 2 and 3 without repetition is:
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Notes on permutations and combinations
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.