SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\begin{gathered} n=10 \\ r=7 \end{gathered}[/tex]
STEP 2: answer question a
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]
To get the answer,
[tex]\begin{gathered} ^{10}C_7=\frac{10!}{(10-7)!7!} \\ =\frac{10\times9\times8\times7!}{3!7!}=\frac{10\times9\times8}{3!}=120 \end{gathered}[/tex]
Hence, 120 different toppings pizza are possible
STEP 3: Answer question b
[tex]=^{75}C_4=\frac{75!}{(75-4)!4!}=1215450[/tex]
Hence, 1215450 mini-boxes are possible
