Answer: 2520
To find the number of ways to arrange something, use factorial (symbol: !) This will multiply the number and all the numbers below it.
E.g. 4! = 4×3×2×1 = 24, which is the number of ways you can arrange 4 objects.
Hence, since there are 10 trees, 10! = 3628800
However, the trees are not unique. This means that some of the trees are the same - like the 'two bald cypress trees'. To fix this, we need to divide by the numbers of non-unique trees (to get rid of duplicates):
[tex]\frac{10!}{5!*3!*2!}[/tex]
(5 linden trees, 3 white birch trees, 2 bald cypress trees)
This will give us the final answer of 2520
(Note: to use factorial on a casio scientific caluclator, press [SHIFT] + [x⁻¹] )
Using arrangements, it is found that the threes can be planted in 2520 ways.
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
If these elements repeat [tex]n_1, n_2, ..., n_n[/tex] times, we have that:
[tex]A_n^{n_1, n_2, ..., n_n} = \frac{n!}{n_1!n_2!...n_n!}[/tex]
In this problem, there are 10 trees, thus [tex]n = 10[/tex].
They repeat 5, 3 and 2 times, thus [tex]n_1 = 5, n_2 = 3, n_3 = 2[/tex].
Then:
[tex]A_{10}^{5,3,2} = \frac{10!}{5!3!2!} = 2520[/tex]
There are 2520 ways to plant the trees.
A similar problem is given at https://brainly.com/question/24648661
