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

10
10

360
360

20
20

60
60

Answer 1

To solve the problem, we need to find the number of different arrangements (permutations) of 3 plants chosen from 5 plants.

We can use the formula for permutations, which is given by:

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

where:
- \( n \) is the total number of items to choose from (in this case, 5 plants),
- \( r \) is the number of items to choose (in this case, 3 plants).

Plugging the values into the formula:

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

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

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

Now substituting these values back into the permutation formula:

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

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

The correct answer is:

**60**