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

$^{30}C _{3} = \frac{30!}{(30 - 3)!3!} \\ = \frac{30!}{27! \times 3!} \\ = \frac{30 \times 29 \times 28 \times 27 \times 26 \times 25 \times . . .\times 3 \times 2 \times 1}{27 \times 26 \times 25 \times . . . \times 3 \times 2 \times 1\times 3 \times 2 \times 1} \\ =5 \times 29 \times 28 \\ =4060$
There are 4060 flavor possibilities.