easy Probability
A release-checked easy problem for training Combinatorics.
A child has a pack of $6$ green and $10$ yellow jellybeans. The child wants to eat $4$ jellybeans, so they grab $4$ jellybeans one-by-one uniformly at random without replacement from the pack. Find the probability that the first two and last two jellybeans agree in colors (not necessarily in order). For example, $GYYG$ and $GGGG$ are both valid, but $GGYG$ is not.
This Probability problem is tagged Combinatorics. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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