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 20 20 360 360 60

Answer 1

To find the number of different arrangements of 3 plants from a total of 5 plants, we can use permutations since the order in which the plants are arranged matters.

The formula for the number of permutations of \( r \) objects from a total of \( n \) objects is given by:

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

In this problem, \( n = 5 \) (the total number of plants) and \( r = 3 \) (the number of plants to choose).

Plugging in these values, we get:

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

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 that Asher can choose out of 5 is \( \boxed{60} \).