#### Case 1: 2 red, 1 green, 1 blue
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- We want the number of 4-bird selections that include **at least one red, one green, and one blue** bird.
- This means the possible color distributions that satisfy this are:
- We calculate the number of ways for each:
- \binom{5}{2} \cdot \binom{7}{1} \cdot \binom{3}{1} = 10 \cdot 7 \cdot 3 = 210
- #### Case 2: 1 red, 2 green, 1 blue
- \binom{5}{1} \cdot \binom{7}{2} \cdot \binom{3}{1} = 5 \cdot 21 \cdot 3 = 315
