Question

sam wants to determine how many possible meals they can make using basic meal building blocks (protein, vegetables, starch). Sam considers a meal to consist of six different building blocks out of 15 possibilities.

[A] Of the 15 meal building blocks there are 5 types of protein, 4 types of starch, and 6 types of vegetables. How many meals can Sam make consisting of 1 type of protein, 2 types of starch, and 3 vegetables?

[B] If all meals are equally likely, what is the probability the meal will consist of the combination in part b?

[C] Let the random variable X= the number of different types of vegetables in the meal. Create a PMF for this random variable. Remember a meal consists of 6 meal building blocks?

Answer 1

A) There can be any of the 5 types of proteins chosen

2 starch can be chosen from 4 type of starch in

3 vegetables can be chosen from 6 type of vegetables in

Hence Total number of  meals Sam can make consisting of 1 type of protein, 2 types of starch, and 3 vegetables = 5* 6 * 20 =600

B) Outr of the 15 building blocks, total number of ways to chooses 6 from 15 is

Hence the required probability =

C)

X	P(X)
0
1
2
3
4
5
6