Multiplication Principle of Counting
What are the possible combinations you can create with the numbers: 2, 4, 7?
E1*E2*E3= E
2*4*7 = 56
N = 7 R = 6. Solve for the amount of possible outcomes if there is no repetition.
𝒏𝑷𝒓 = 𝒏!/(𝒏 − 𝒓)!
𝒏𝑷𝒓 =7!/(7 - 6)!
𝒏𝑷𝒓 = 5040
It refers to a situation involving chance or probability that produces an event.
Experiment
You roll a die twice. What is the possibility of getting the same number twice in a row?
𝑷(𝑬) = 𝑛 (𝐸)/ 𝑛 (𝑆)
𝑷(𝑬) = 6 (number in a die)/36 (number of possible outcomes)
𝑷(𝑬) = 1/6
This is probability based on experience and judgment of the person to determine whether a specific outcome is likely to occur.
Theoretical or Classical Probability
How many combinations can you create with the numbers: 7, 10, 17?
E1*E2*E3= E
7*10*17 = 1,190
There are over 24 different clothes in your wardrobe. 12 of it are shirts, 6 of it are pants, 6 of it are shoes. What is the permutation for your fashion sense?
𝒏𝑷𝒓 = 𝒏!/(𝒏 − 𝒓)!
𝒏𝑷𝒓 =24!/(24 - 3)!
𝒏𝑷𝒓 = 12144
A counting technique which refers to the arrangement (or ordering) of a set of objects, from first to last, where the order in which the objects are selected does matter.
Permutation
You go gambling at a roulette wheel with there being 37 different outcomes (0-36). What are the chances of getting the same number twice?
37*37 = 1369
37/1369 = 0.027 or 2.7%
When one event occurs, the other cannot, and vice versa.
Mutually Exclusive Events.
There are 4 types of vehicles available for you to drive with 13 different colors available to choose from and 5 different accessories for you to add onto it. How many combinations of vehicles can you create?
E1*E2*E3= E
4*13*5 = 260
In 𝒏𝑷𝒓, what does 𝒏 mean?
𝒏 is the number of objects to choose from.
What are the two kinds of events?
Simple Event & Compound Event
What are your chances in winning a color game with 6 colors and you can only pick one?
1/6 or a 0.167%
It refers to one or more of the possible outcomes of a single trial of an experiment.
Event
A milk tea shop has 5 different cup sizes, 15 different flavors and 12 different toppings choices. How many possible milk tea combinations are possible?
E1*E2*E3= E
5*15*12 = 900
There are 30 different food items to eat. 6 are drinks, 6 are meals, 3 are appetizers, and 9 are dessert. What is the permutation for the food you have?
𝒏𝑷𝒓 = 𝒏!/(𝒏 − 𝒓)!
𝒏𝑷𝒓 = 30!/(30 − 4)!
𝒏𝑷𝒓 = 657720
A selection of objects from a collection in any order as oppose to permutations which deal with the ordered arrangements of objects.
Combination
Out there in the world of 8 billion people is the person for you. What are the chances that you find them?
1/8,000,000,000 or 0.0000000125 or 0.00000125%
Based on examining past data and using logical and mathematical equations involving the data to determine the likelihood of an independent event occurring.
Empirical or Experimental Probability
Clementine and Louis go to the mall to buy something for their anniversary. There are 5 types of cake available for them to eat together they also spot 6 different matching gifts that they can choose one of to give each other, along with 8 different pianos that they can choose one of to play with. How many combinations of gifts can they have that they can buy for both of them?
E1*E2*E3= E
5*6*8 = 240
What is the difference between a permutation and a combination?
The order of the items are important in a permutation where as in a combination it does not.
It states that: If there are n1 possible number of outcomes/ways for event 𝐸1; and n2 possible number of outcomes/ways for event 𝐸2, then the possible number of outcomes/ways for both events is (n1 ∗ n2) number of outcomes/ways. It only works when all choices are independent of each other.
Multiplication Principle of Counting
(Double Points)
There is a glass bridge in front of you that you have to get across and each glass you jump on has a 50% chance of being the right one. There seems to be 18 glass panels that you have to jump on to. What are the chances you get across first try?
50%18 = 1/262144 or 0.000003815% or 0.00038%
It is what is used to describe the phenomenon of chance or randomness of events to occur.
Probability