Question

# sam wants to determine how many possible meals they can make using basic meal building blocks...

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?

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

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