luis is packing a bag for vacation. he has 9 unique shirts, but he can only fit 5 in his bag. how many…

Explanation:

Step1: Identify combination formula

The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen. Here, $n = 9$ and $r=5$.

Step2: Calculate factorial values

$n!=9! = 9\times8\times7\times6\times5\times4\times3\times2\times1$, $r!=5!=5\times4\times3\times2\times1$, and $(n - r)!=(9 - 5)!=4!=4\times3\times2\times1$. $C(9,5)=\frac{9!}{5!(9 - 5)!}=\frac{9\times8\times7\times6\times5!}{5!\times4!}=\frac{9\times8\times7\times6}{4\times3\times2\times1}$.

Step3: Simplify the expression

$\frac{9\times8\times7\times6}{4\times3\times2\times1}=\frac{9\times8\times7\times6}{24}=126$.

Answer:

126