Question

14 a pizza shop offers eight different toppings of pizza. grace chooses two toppings for a pizza. how many different possible choices could she make? 28 57 30 27

Explanation:

Step1: Identify the problem type

This is a combination problem where we need to find the number of ways to choose 2 toppings out of 8, and the order of choosing doesn't matter. The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 8 \) (total number of toppings) and \( k=2 \) (number of toppings to choose).

Step2: Calculate the factorial values

First, calculate the factorials:

• \( n!=8!=8\times7\times6\times5\times4\times3\times2\times1 \)
• \( k!=2!=2\times1 \)
• \( (n - k)!=(8 - 2)!=6!=6\times5\times4\times3\times2\times1 \)

Step3: Substitute into the combination formula

\[

$$\begin{align*} C(8, 2)&=\frac{8!}{2!(8 - 2)!}\\ &=\frac{8\times7\times6!}{2\times1\times6!}\\ &=\frac{8\times7}{2\times1}\\ &=\frac{56}{2}\\ & = 28 \end{align*}$$

\]

Answer:

28