Question

There are 30 flavors and you can mix up to 3 of them. How many flavor possibilities are there? You can't mix the same flavors more than once in one drink. Show your work.

Answer 1

`^(30)C _(3) = (30!)/((30 - 3)!3!) \\ = (30!)/(27! * 3!) \\ = (30 * 29 * 28 * 27 * 26 * 25 * . . .* 3 * 2 * 1)/(27 * 26 * 25 * . . . * 3 * 2 * 1* 3 * 2 * 1) \\ =5 * 29 * 28 \\ =4060`
There are 4060 flavor possibilities.