\boxed{720}
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- Within the block, the 3 public health officials can be arranged among themselves in $ 3! = 6 $ ways.
- Thus, the total number of arrangements is:
- \times 6 = 720
- Question: A palynologist has 5 red pollen grains, 3 green pollen grains, and 2 blue pollen grains. If she randomly selects 6 grains from the bag without replacement, what is the probability that exactly 2 red, 2 green, and 2 blue grains are selected?
- We begin by computing the total number of ways to choose 6 grains from the total of $ 5 + 3 + 2 = 10 $ grains:
- \binom{10}{6} = 210
