We appreciate your visit to A friend of mine is giving a dinner party His current wine supply includes 9 bottles of zinfandel 7 of merlot and 11 of cabernet. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Answer: a) 783 ways; b) 593775 ways
Step-by-step explanation:
a) Your friend wants to select 3 zinfandel out of 9 from the supply in a particular order, which means:
[tex]P_{n,r} = \frac{n!}{(n-r)!}[/tex]
[tex]P_{9,3} = \frac{9!}{(9 - 3)!}[/tex]
[tex]P_{9,3} = \frac{9.8.7.6!}{6!}[/tex]
[tex]P_{9,3}[/tex] = 783
In the dinner party, the friend will have 783 ways of serving the zinfandel.
b) Now, your friend want to select 6 bottles out of 30 in no particular order and randomly selected. So:
[tex]C_{n,r} = \frac{n!}{r!(n - r)!}[/tex]
[tex]C_{30,6} = \frac{30!}{6!.24!}[/tex]
[tex]C_{30,6} = \frac{30.29.28.27.26.25.24!}{6.5.4.3.2.1.24!}[/tex]
[tex]C_{30,6}[/tex] = 593775
If you select 6 bottles randomly from 30, you will have 593775 ways of doing it.
Thanks for taking the time to read A friend of mine is giving a dinner party His current wine supply includes 9 bottles of zinfandel 7 of merlot and 11 of cabernet. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
