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)
360
10
60
20

Answer 1

To find the number of different arrangements 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, the 5 plants), and \(r\) is the number of items to arrange (in this case, 3 shaded spots).

Thus, we can substitute \(n = 5\) and \(r = 3\) into the formula:

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

Now we calculate \(5!\) and \(2!\):

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

Now we can calculate \(P(5, 3)\):

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

Therefore, the number of different arrangements of 3 plants chosen from 5 is \(60\).

The answer is \(60\).