Question

There are 6 red apples, 4 yellow apples, and 2 green apples in a bucket. Maria will chose two apples at random without replacement. What is the probability that Maria will choose a red apple and a green apple?

Answer 1

\[\frac{\dbinom{6}{1}\times \dbinom{2}{1}}{\dbinom{12}{2}}\]

Answer 2

\(\binom{6}{1}=6,\binom{2}{1}=2\) so the only real calculation is \(\binom{12}{2}=\frac{12\times 11}{2}=66\)

Answer 3

therefore your answer is
\[\frac{6\times 2}{66}=\frac{2}{11}\]

Answer 4

you can also compute this as
\[\frac{6}{12}\times \frac{2}{11}+\frac{2}{12}\times \frac{6}{11}\]a nd get the same thing