A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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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. **Question Help:**
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Transcribed Image Text:**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. **Question Help:**
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