Thus, the probability is $ \boxed{\frac{2}{5}} $.

February 22, 2026

$Thus, the probability is $ \boxed{\frac{2}{5}} $.$

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Total number of ways to choose 3 vials from 6:
To get one vial of each color, we choose one red, one blue, and one green. There are 2 choices for each color:
\times 2 \times 2 = 8 \text{ favorable outcomes}
Question: A cognitive mapping specialist studies decision paths in a grid where each step is either forward or right. If a path from point A to point B requires exactly 4 forward moves and 3 right moves, and each move is chosen at random, what is the probability that the first move is forward and the last move is right?
Total number of valid paths: arrange 4 F’s and 3 R’s →
\text{Total paths} = \binom{7}{4} = 35

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