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 that he randomly plants the trees so that all 44 cypress trees are next to each other and all 44 dogwoods are next to each other? Express your answer as a fraction or a decimal number rounded to four decimal places.

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Priatouri Priatouri · Answer 1 · 2020-06-26T04:52:45+02:00

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]