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Combinations - Problem Solving


Suppose \(10\) points are drawn on a plane such that exactly \(4\) of the points are collinear and among the remaining points, no three points are collinear. How many distinct lines can be drawn by connecting any \(2\) among these \(10\) points?

How many ways can the integers \(1,2,3,4,5,6\) be arranged such that \(2\) is adjacent to either 1 or 3?

Details and assumptions

2 could be next to both 1 and 3.

Ten players were entered into a badminton tournament. The first round consisted of 5 matches, with each player in one match. How many different ways could the 10 players be matched against each other?

How many ways are there to pick two distinct numbers from \(1\) to \(11\) such that the sum of the two numbers is even?

The baseball teams SeaWolves and Raptors are playing for the championship. If there are \(12\) players on the SeaWolves and \(11\) players on Raptors, how many ways are there to choose \(2\) players from the same team?


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