holly chooses seven out of nine plants for the front of her house with the remaining plants to be used on…
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?\n7\n9\n21\n36
Answer
Explanation:
Step1: Identify combination formula
We use the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen. Here, $n = 9$ and $r=7$.
Step2: Calculate factorial values
$n!=9! = 9\times8\times7\times6\times5\times4\times3\times2\times1$, $r!=7!=7\times6\times5\times4\times3\times2\times1$, and $(n - r)!=(9 - 7)!=2!=2\times1$. Then $C(9,7)=\frac{9!}{7!(9 - 7)!}=\frac{9!}{7!2!}=\frac{9\times8\times7!}{7!\times2\times1}$.
Step3: Simplify the expression
Cancel out the $7!$ terms in the numerator and denominator. We get $\frac{9\times8}{2\times1}=\frac{72}{2}=36$.
Answer:
36