Permutations vs combinations
Use permutations when order matters, such as arranging letters, race finishing positions, PINs, or schedules. Use combinations when order does not matter, such as choosing a committee or lottery numbers.
Real-world examples
Permutations answer questions like how many ways three medals can be awarded from ten runners. Combinations answer questions like how many teams of three can be chosen from ten people.
Pascal's triangle and combinations
Each row of Pascal's triangle contains combination values. Row n gives C(n,0), C(n,1), C(n,2) and so on, with each value formed by adding the two values directly above it.