1. Jerry is having bread and drinks for breakfast, He can choose between ham sandwich, toasted bread, and pandesal. For drinks, he can choose either coffee, milk or orange juice. How many selections will he have?
2. An athlete is making a healthy protein shake from fruits, nuts, and vegetables. if there are 4 available nuys, 7 available fruits, and 5 available vegetables to choose from, how many possible flavors of shake can be made?
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Question & Answer:
1. Jerry is having bread and drinks for breakfast, He can choose between ham sandwich, toasted bread, and pandesal. For drinks, he can choose either coffee, milk or orange juice. How many selections will he have?
# of bread choices = 3
# of drink choices = 3
Total ways of selecting a bread and a drink is,
3 × 3 = 9 ways
Proof using Tree Diagram,
Ham Sandwich + Coffee or Milk or Orange Juice --> 3 combinations
e.g.,
Ham Sandwich + Coffee
Ham Sandwich + Milk
Ham Sandwich + Orange Juice
Toasted Bread + Coffee or Milk or Orange Juice --> 3 combinations
Pandesal + Coffee or Milk or Orange Juice --> 3 combinations
Add all the outcomes of the Tree Diagram,
3 + 3 + 3 = 9 ways or combinations
2. An athlete is making a healthy protein shake from fruits, nuts, and vegetables. if there are 4 available nuys, 7 available fruits, and 5 available vegetables to choose from, how many possible flavors of shake can be made?
Using same concept as #1, the total number of ways to mix the 3 ingredients is,
# of Nuts = 4
# of Fruits = 7
# of Vegetables = 5
4 × 7 × 5 = 140 ways
You can also prove this using Tree diagram and you will end up with 140 combinations.
* as always, double check my answers for errors or carelessness.
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