Question

HELP!!!!!

Answer 1

Answer:

$\dfrac{2}{91}$

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:

$C^5_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!\cdot 2!}=\dfrac{3!\cdot 4\cdot 5}{3!\cdot 2}=10$

Find the number of choices 3 different toppings:

$C^{15}_3=\dfrac{15!}{3!(15-3)!}=\dfrac{15!}{3!\cdot 12!}=\dfrac{12!\cdot 13\cdot 14\cdot 15}{12!\cdot 2\cdot 3}=13\cdot 7\cdot 5=455$

Hence, he probability that your group orders only meat toppings is

$\dfrac{10}{455}=\dfrac{2}{91}$