Choc chip -- 12
oatmeal ---- 12
no-bake ---- 12
peanut butter --12
gingerbread ---12
Sample space = C(60,6)
selections of six gingerbread from 12 = C(12,6)
prob = C(12,6)/(C(60,6) = .000018456
oatmeal ---- 12
no-bake ---- 12
peanut butter --12
gingerbread ---12
Sample space = C(60,6)
selections of six gingerbread from 12 = C(12,6)
prob = C(12,6)/(C(60,6) = .000018456
In this case, you have a total of 60 cookies, and the gingerbread cookies are one kind out of five dozen. Since each dozen contains 12 cookies, the number of gingerbread cookies is:
5 dozen * 12 cookies/dozen = 60 gingerbread cookies.
Now, let's calculate the probability. Since you are picking six cookies from the tin randomly, the probability of picking all gingerbread cookies can be calculated by finding the ratio of the favorable outcomes (picking all gingerbread cookies) to the total possible outcomes (picking any six cookies).
The favorable outcomes are picking all six gingerbread cookies, which is 60 choose 6. This can be calculated as:
(60!)/(6!(60-6)!) = 50,063,860.
The total possible outcomes are picking any six cookies from the tin, which is 60 choose 6. This can be calculated as:
(60!)/(6!(60-6)!) = 50,063,860.
Now, divide the number of favorable outcomes by the total possible outcomes to get the probability:
50,063,860 / 50,063,860 = 1.
Therefore, the probability of picking all gingerbread cookies is 1 or 100%.