Question

20 a pizza restaurant offers nine choices of vegetarian toppings for pizza. in how many ways can you choose four toppings?
○ 362,880
○ 126
○ 15,120
○ 3024

Explanation:

Step1: Identify combination formula

We use combinations since order doesn't matter for toppings:
$$C(n,k)=\frac{n!}{k!(n-k)!}$$
where $n=9$ (total toppings), $k=4$ (toppings to choose)

Step2: Substitute values into formula

$$C(9,4)=\frac{9!}{4!(9-4)!}=\frac{9!}{4!5!}$$

Step3: Simplify the factorial expression

$$\frac{9\times8\times7\times6\times5!}{4\times3\times2\times1\times5!}=\frac{9\times8\times7\times6}{4\times3\times2\times1}$$

Step4: Calculate the final value

$$\frac{3024}{24}=126$$

Answer:

126