Question

Question
Use permutations to solve the following problem. If 5 plants thrive in shade and Asher’s garden has three shaded spots, then how many different arrangements of 3 could he choose out of those 5 plants?(1 point)
Responses

360
360

20
20

10
10

60

Answer 1

To determine the number of different arrangements of 3 plants chosen out of 5, we can use the formula for permutations, because the order in which we arrange the plants matters.

The formula for permutations is given by:

\[
P(n, r) = \frac{n!}{(n - r)!}
\]

where
- \( n \) is the total number of items (in this case, plants),
- \( r \) is the number of items to arrange.

In this problem, \( n = 5 \) (the number of plants) and \( r = 3 \) (the number of shaded spots).

Plugging in the values:

\[
P(5, 3) = \frac{5!}{(5 - 3)!} = \frac{5!}{2!}
\]

Calculating \( 5! \) and \( 2! \):

\[
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
\]
\[
2! = 2 \times 1 = 2
\]

Now substituting back into the permutation formula:

\[
P(5, 3) = \frac{120}{2} = 60
\]

Thus, the number of different arrangements of 3 plants out of 5 is **60**.

Therefore, the correct response is **60**.