Question

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?

Explanation:

Step1: Identify combination formula

Since order doesn't matter, use combinations: $C(n,k)=\frac{n!}{k!(n-k)!}$ where $n=9$, $k=7$.

Step2: Substitute values

$C(9,7)=\frac{9!}{7!(9-7)!}=\frac{9×8×7!}{7!×2×1}$

Step3: Simplify expression

Cancel $7!$, calculate $\frac{9×8}{2×1}=36$

Answer:

36