Question

algebra i b-cr
pre-test complete
time remaining
58:42
holly chooses seven out of nine plants for the front of her house with the remaining plants to be used on the side of the house.
if order does not matter, in how many ways can she choose the plants for the front of the house?
○ 7
○ 9
○ 21
○ 36

Explanation:

Step1: Recognize combination problem

Since order does not matter, we use the combination formula $C(n,k)=\frac{n!}{k!(n-k)!}$, where $n=9$ (total plants) and $k=7$ (plants to choose).

Step2: Simplify combination (use symmetry)

Note that $C(n,k)=C(n,n-k)$, so $C(9,7)=C(9,2)$.

Step3: Calculate $C(9,2)$

$C(9,2)=\frac{9!}{2!(9-2)!}=\frac{9\times8}{2\times1}$

Step4: Compute final value

$\frac{9\times8}{2\times1}=36$

Answer:

36 (Option D: 36)