Question

for a yogurt bowl, 3 fruit toppings can be chosen from 6 options: blueberries, raspberries, kiwi, peach, pear, and watermelon. how many unique 3 - topping combinations are possible?
$_{6}c_{3}=\square$
hint:
$_{n}c_{r}=\frac{_{n}p_{r}}{r!}$

Explanation:

Step1: Recall combination formula

Combination formula: $C(n, r) = \frac{n!}{r!(n-r)!}$ where $n=6$, $r=3$.

Step2: Calculate factorials

$6! = 720$, $3! = 6$, $(6-3)! = 6$.

Step3: Compute the value

$C(6,3) = \frac{720}{6 \times 6} = 20$.

Answer:

20