Answer:
[tex]\dfrac{2}{91}[/tex]
Step-by-step explanation:
There are 15 toppings: 5 toppings are meat and 10 toppings are vegetable.
You and two friends form a group of 3 people.
Find the number of choices 3 different meat toppings:
[tex]C^5_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!\cdot 2!}=\dfrac{3!\cdot 4\cdot 5}{3!\cdot 2}=10[/tex]
Find the number of choices 3 different toppings:
[tex]C^{15}_3=\dfrac{15!}{3!(15-3)!}=\dfrac{15!}{3!\cdot 12!}=\dfrac{12!\cdot 13\cdot 14\cdot 15}{12!\cdot 2\cdot 3}=13\cdot 7\cdot 5=455[/tex]
Hence, he probability that your group orders only meat toppings is
[tex]\dfrac{10}{455}=\dfrac{2}{91}[/tex]
