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# Combinations

If a coin is flipped twenty times, how many ways are there to get exactly ten tails and ten heads?

# 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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