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counting and probability senior

Problem

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.
Solution
We can count the number of ways to choose a group of 4 green and 2 red peppers and the number of ways to choose 5 green and 1 red peppers. These are and . The total number of ways the cook can choose peppers is . Therefore, the probability that out of six randomly chosen peppers at least four will be green is .
Final answer
\frac{47}{1001}