You have a craving for Mrs. Fields gourmet cookies. You have a choice of oatmeal raisin, macadamia nut, triple chocolate, cinnamon sugar, chocolate chip, and peanut butter. If you must choose at least one cookie:

1) how many ways is this possible

2) what is the probability that you do not take cookies that contain chocolate

Is my solution below correct?:

1) 6C1 + 6C2 + 6C3 + 6C4 + 6C5 + 6C6 = 63

2) The number of ways to not choose chocolate is

4C1 + 4C2 + 4C3 + 4C4 = 15

Probability to not choose chocolate is 15/63 = 23.8

I solved this way because it said I have to choose at least one cookie so therefore I could choose 1 cookie that's not chocolate or 2 Cookies that aren't chocolate or 3 or 4.

Is my solution above correct?