### Instruction: A cook has 10 red peppers and 5 green peppers. If the cook selects 6 peppers at random, what is the probability that he selects at least 4 green peppers? Express your answer as a common fraction.### Response: I need to find the total number of ways to select 6 peppers out of 15, and the number of ways to select at least 4 green peppers out of 15.
I can use the combination formula to count the number of ways to choose k items out of n: C(n, k) = n! / (k! (n - k)!).
The total number of ways to select 6 peppers out of 15 is C(15, 6) = 15! / (6! 9!) = 5005.
The number of ways to select exactly 4 green peppers out of 15 is C(5, 4) * C(10, 2) = 5 * 45 = 225.
The number of ways to select exactly 5 green peppers out of 15 is C(5, 5) * C(10, 1) = 1 * 10 = 10.
The number of ways to select exactly 6 green peppers out of 15 is C(5, 6) * C(10, 0) = 0 * 1 = 0.
The number of ways to select at least 4 green peppers out of 15 is the sum of the above three cases: 225 + 10 + 0 = 235.