Combinations - Problem Solving


Suppose 1010 points are drawn on a plane such that exactly 44 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 22 among these 1010 points?

How many ways can the integers 1,2,3,4,5,61,2,3,4,5,6 be arranged such that 22 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 11 to 1111 such that the sum of the two numbers is even?

The baseball teams SeaWolves and Raptors are playing for the championship. If there are 1212 players on the SeaWolves and 1111 players on Raptors, how many ways are there to choose 22 players from the same team?


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