Question

at an ice cream shop, customers can choose 3 flavors from 8 available flavors. how many different 3-flavor combinations are possible?
$_{8}c_{3} = \boxed{?}$
hint:
$_{n}c_{r}=\frac{_{n}p_{r}}{r!}$

Explanation:

Step1: Recall combination formula

The combination formula is $C(n, r) = \frac{n!}{r!(n-r)!}$, where $n=8$ and $r=3$.

Step2: Calculate factorials

$8! = 8×7×6×5!$, $3! = 6$, $(8-3)! = 5!$. Substitute: $C(8,3) = \frac{8×7×6×5!}{3!×5!} = \frac{8×7×6}{6}$.

Step3: Simplify the expression

Cancel 6: $8×7 = 56$.

Answer:

56