Question

Tim is choosing a shrub and a rase for his garden.
at the garden centre there are 266 different types os shrubs and some rose trees.
Tim works out that there are 266 different ways for him to choose one shrub ans one rose tree
if Tim is correct with his figure of 266 different ways, how many rose trees are there at the garden centre?​

Answer 1

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 $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem:

• The figures are composed by shrubs and roses.

• For the shrub, there are 266 options, hence $n_1 = 266$.

• For the figure, there are also 266 options, hence $N = 266$.

• For the rose, there are $n_2$ options.

Hence:

$N = n_1 \times n_2$

$266 = 266n_2$

$n_2 = \frac{266}{266}$

$n_2 = 1$

Hence, there is 1 rose tree at the garden center.

To learn more about the Fundamental Counting Theorem, you can take a look at