Question

Suppose we want to choose 6 colors, without replacement, from 10 distinct colors.

Answer 1

There are 10 choices for the first color, 9 choices for the second color (since we've already picked one), and so on down to 5 choices for the sixth color. This gives us:

10 × 9 × 8 × 7 × 6 × 5 = 151,200

So there are 151,200 ways to choose 6 colors without replacement from 10 distinct colors.