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 arrangments can Amanda make? Amanda can make different arrangements. Question Help: Message instructor
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 arrangments can Amanda make? Amanda can make different arrangements. Question Help: Message instructor
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Not sure how to solve this
![**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:**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1cff5689-7bd0-475a-a8ff-9b9e13f1a527%2Fcd13129d-731e-494f-af5c-d61bde5a83ca%2Fu39lhjr_processed.jpeg&w=3840&q=75)
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:**
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON