How Does the Number of Metro Stations Affect the Color of Connecting Lines?

In summary, permutations and combinations are mathematical concepts that involve counting the number of ways to arrange or select objects from a given set. Permutations refer to the number of ways to arrange objects in a specific order, while combinations refer to the number of ways to select a subset of objects without regard to order. The formula for calculating permutations is nPr = n! / (n-r)!, while the formula for calculating combinations is nCr = n! / (r!*(n-r)!). The main difference between permutations and combinations is that permutations take into account the order of objects, while combinations do not. They have many real-world applications, such as in probability, statistics, and combinatorics, and are useful for solving problems involving counting
  • #1
DaalChawal
87
0
Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is 99 times the number of blue lines, then the value of n is
 
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  • #2
Let's pick n=4.
How many blue lines and how many red lines?
What if n=5?
How many for an arbitrary n?
 

Related to How Does the Number of Metro Stations Affect the Color of Connecting Lines?

1. What is the difference between permutation and combination?

Permutation and combination are both methods used to count the number of possible outcomes in a given situation. The main difference between them is that in permutation, the order of the elements matters, while in combination, the order does not matter. For example, if we have the letters A, B, and C, the permutations would be ABC, ACB, BAC, etc., while the combinations would be ABC, ACB, BCA, etc.

2. How do I calculate the number of permutations or combinations?

The formula for calculating permutations is n! / (n-r)!, where n is the total number of items and r is the number of items chosen. For combinations, the formula is n! / (r!(n-r)!). It is important to note that the exclamation mark (!) represents the factorial function, which means multiplying the number by all the numbers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

3. What is the purpose of using permutations and combinations?

Permutations and combinations are used to solve problems related to probability and counting. They are commonly used in fields such as mathematics, statistics, and computer science to determine the number of possible outcomes in a given scenario. They can also be used to calculate the probability of a particular event occurring.

4. Can permutations and combinations be used interchangeably?

No, permutations and combinations serve different purposes and cannot be used interchangeably. As mentioned earlier, permutations take into account the order of the elements, while combinations do not. Using the wrong method can lead to incorrect results, so it is essential to understand the difference between them and use the appropriate one for the given problem.

5. How can I apply permutations and combinations in real-life situations?

Permutations and combinations have various real-life applications, such as in gambling, genetics, and sports. For example, in a lottery, the order of the numbers drawn is essential, so permutations would be used to calculate the odds of winning. In genetics, combinations are used to determine the possible genotypes of offspring from two parents. In sports, combinations can be used to determine the number of possible game outcomes in a tournament.

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