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![**Flower Arrangement Combinatorics**
Amanda is making flower arrangements for a party and has a choice of 7 roses, 13 orchids, and 10 carnations. Amanda would like to have four roses, six orchids, and eight carnations in each arrangement. How many different arrangements can Amanda make?
**Calculate the Combinations:**
- **Roses:** Choose 4 out of 7 \( \binom{7}{4} \)
- **Orchids:** Choose 6 out of 13 \( \binom{13}{6} \)
- **Carnations:** Choose 8 out of 10 \( \binom{10}{8} \)
Multiply the combinations for the total number of arrangements:
\[ \text{Total Arrangements} = \binom{7}{4} \times \binom{13}{6} \times \binom{10}{8} \]
Amanda can make _______ different arrangements.
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