+1246 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.
+4623 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 (54)(102)=5⋅45=225 and (55)(101)=10. The total number of ways the cook can choose peppers is (156)=5005. Therefore, the probability that out of six randomly chosen peppers at least four will be green is 2355005=471001.
