Thank you for visiting Rafael is planting trees along his driveway and he has 44 cypress trees and 44 dogwoods to plant in one row What is the probability. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final answer:
The probability that Rafael randomly plants the trees so that all cypress trees are next to each other and all dogwoods are next to each other is approximately 0.0019753.
Explanation:
To calculate the probability, we need to determine the total number of possible outcomes and the number of outcomes where all the cypress trees are next to each other and all the dogwoods are next to each other. Since the cypress trees and dogwoods must be planted in one row, there are 45 possible positions (44 spaces between the trees and 1 space on each end). The number of outcomes where all the cypress trees are together is 2 (either all at the front or all at the back), and the number of outcomes where all the dogwoods are together is also 2. So the probability is 2/45 * 2/45 = 4/2025, which can also be expressed as approximately 0.0019753.
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Rewritten by : Jeany
Answer:
The probability is [tex]= 7.62 \times 10^{-26}[/tex]
Step-by-step explanation:
Given number of cypress trees = 44
Given number of dogwoods trees = 44
Now assume all cypress trees as 1 unit and dogwood trees as 1 unit.
So , there are 2 units
Now, the 2 units can be arranged in 2! ways.
here internally the 44 dogwoods and 44 cypress trees will not shuffled( as all are the same) we have
P( all trees of 44 cypress are next to each other and all 44 dogwoods trees are next to each other)
[tex]= \frac{2}{\frac{88!}{44!^{2}}} \\= 7.62 \times 10^{-26}[/tex]
