Question

A​ golf-course architect has five linden​ trees, three white birch​ trees, and two bald cypress trees to plant in a row along a fairway. In how many ways can the landscaper plant the trees in a​ row, assuming that the trees are evenly​ spaced?

Answer 1

Answer:2520 i used a caculater also i want brainliest

Step-by-step explanation:

Answer 2

Answer: 2520

Explanation

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):

$\frac{10!}{5!*3!*2!}$

(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] )