Using the Fundamental Counting Theorem, it is found that there is 1 rose tree at the garden center.
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
- The figures are composed by shrubs and roses.
- For the shrub, there are 266 options, hence [tex]n_1 = 266[/tex].
- For the figure, there are also 266 options, hence [tex]N = 266[/tex].
- For the rose, there are [tex]n_2[/tex] options.
Hence:
[tex]N = n_1 \times n_2[/tex]
[tex]266 = 266n_2[/tex]
[tex]n_2 = \frac{266}{266}[/tex]
[tex]n_2 = 1[/tex]
Hence, there is 1 rose tree at the garden center.
To learn more about the Fundamental Counting Theorem, you can take a look at
