Question

HELP!!!!!

You and two friends visit a pizza shop. There are 15 toppings. 5 toppings are meat and the rest are vegetable. Each of you order a different topping (no repeats) at random. What is the probability that your group orders only meat toppings?

Answer 1

Answer: 2/91 is the answer

Answer 2

`(2)/(91)`

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=(5!)/(3!(5-3)!)=(5!)/(3!\cdot 2!)=(3!\cdot 4\cdot 5)/(3!\cdot 2)=10`

Find the number of choices 3 different toppings:

`C^(15)_3=(15!)/(3!(15-3)!)=(15!)/(3!\cdot 12!)=(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

`(10)/(455)=(2)/(91)`