Permutations and Combinations
Permutations: How many rainbows can you draw with these colors (red, orange, yellow, green, blue)? Each rainbow can only have 3 colors, no repeated colors.
Where n is the number of things to choose from, and you choose r of them (No repetition, order matters) n!/(n-r)!
Permutations with Repetition: Each passcode is 5 numbers long. How many passcodes are possible?
Combinations: How many ways can a group of three students be selected from a class of 21 students?
(21!)/(18!)(3!) = 1330 "n choose r" Where n is the number of things to choose from, and you choose r of them (No repetition, order doesn't matter)
Combinations with Repetition: You get 4 scoops of ice cream, how many different combinations can you make from Chocolate, Vanilla, and Strawberry?
"(n + r - 1) choose r"