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# HELP!

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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.

Apr 28, 2018

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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 $$\binom{5}{4}\binom{10}{2}=5\cdot45=225$$ and $$\binom{5}{5}\binom{10}{1}=10$$. The total number of ways the cook can choose peppers is $$\binom{15}{6}=5005$$. Therefore, the probability that out of six randomly chosen peppers at least four will be green is $$\frac{235}{5005}=\boxed{\frac{47}{1001}}$$.

Apr 28, 2018