To solve this problem, we need to consider all possible combinations where Cherry chooses at least one of each type of ornament. The types are wooden animals (W), sea-shells (S), and pottery ducks (D).

We can break down the combinations as follows:

1. 1 W, 1 S, 3 D: The number of ways to choose 1 wooden animal is 6, 1 sea-shell is 4, and 3 pottery ducks is \(\binom{3}{3} = 1\). Total = \(6 \times 4 \times 1 = 24\).
2. 1 W, 3 S, 1 D: The number of ways to choose 1 wooden animal is 6, 3 sea-shells is \(\binom{4}{3} = 4\), and 1 pottery duck is 3. Total = \(6 \times 4 \times 3 = 72\).
3. 3 W, 1 S, 1 D: The number of ways to choose 3 wooden animals is \(\binom{6}{3} = 20\), 1 sea-shell is 4, and 1 pottery duck is 3. Total = \(20 \times 4 \times 3 = 240\).
4. 1 W, 2 S, 2 D: The number of ways to choose 1 wooden animal is 6, 2 sea-shells is \(\binom{4}{2} = 6\), and 2 pottery ducks is \(\binom{3}{2} = 3\). Total = \(6 \times 6 \times 3 = 108\).
5. 2 W, 1 S, 2 D: The number of ways to choose 2 wooden animals is \(\binom{6}{2} = 15\), 1 sea-shell is 4, and 2 pottery ducks is \(\binom{3}{2} = 3\). Total = \(15 \times 4 \times 3 = 180\).
6. 2 W, 2 S, 1 D: The number of ways to choose 2 wooden animals is \(\binom{6}{2} = 15\), 2 sea-shells is \(\binom{4}{2} = 6\), and 1 pottery duck is 3. Total = \(15 \times 6 \times 3 = 270\).

Adding all these combinations gives the total number of selections:

\(24 + 72 + 240 + 108 + 180 + 270 = 894\).