Multiplication Principle
Definition of
Multiplication Principle
·
Multiplication
Principle states: If an event occurs in m ways and another event occurs
independently in n ways, then the two events can occur in m × n ways.
Solved Example on
Multiplication Principle
Ali can choose 6
types of ice cream for his desserts while Alex can choose 6 different types of
chocolate as his desserts. So how many possible outcomes is there for their choices?
The answer is 6 (choice that can be made by Ali) X 6 ( other choices that can be made by Alex ) = 36. There are 6 different chocolates that Alex can choose from for every one of 6 ice creams that Ali can choose to form the combination. So there is 36 combinations for this situation.
The answer is 6 (choice that can be made by Ali) X 6 ( other choices that can be made by Alex ) = 36. There are 6 different chocolates that Alex can choose from for every one of 6 ice creams that Ali can choose to form the combination. So there is 36 combinations for this situation.
Addition Principle
Definition of Addition
Principle
·
Addition Principle
states: If an event can occurs in m ways and n ways, then the one events can occur in m + n ways.
Solved Example on
Multiplication Principle
Ali can now choose
his one dessert from 6 flavours of ice creams and 6 types of chocolates as his
dessert. How many possible outcome is
there for this situation?
The answer is 6 (types of ice cream) + 6 (types of chocolates) = 12. Ali can choose as he wills from 12 desserts made up from 6 ice creams and 6 chocolates.
The answer is 6 (types of ice cream) + 6 (types of chocolates) = 12. Ali can choose as he wills from 12 desserts made up from 6 ice creams and 6 chocolates.
Combination
Principle
Definition of Combination
Principle
·
A combination of both
Addition Principle and Multiplication Principle?
Solved Example on
Multiplication Principle
Ali wants to have his
lunch in a food court. He wants to have only 1 or 2 meals from the vast variety
of dishes served in the food court. He can choose from 5 Chinese cuisines, 6
Malay cuisines, and 8 types of desserts. So what choices does he have?
If he only wishes to
have 1 meal, he can choose from 5 (Chinese cuisines) + 6 ( Malay cuisine) + 8
(desserts) = 19 choices.
If he wishes to have
2 meals of different cuisine, he can choose from 19 X 18 = 342 combinations of
meals.
So, if he wishes to have only 1 or 2 meals from the food court, there is 342 + 19 = 361 ways he can have his lunch in the food court.
So, if he wishes to have only 1 or 2 meals from the food court, there is 342 + 19 = 361 ways he can have his lunch in the food court.
Permutation
Definition: A way, esp. one of several possible variations, in
which a set or number of things can be ordered or arranged especially in linear
order.
Formula: n P
r = n! / (n-r)!
Problem
Solving
When A,B,C, D and E are lined up for photo shooting
sessions, but there’s only 3 persons are allowed. How many different positions
can they create for the session?
The answer is 5 X 4 X 3 which is 60 ways.
Or
120 (5!) / 2
(2!) = 60.
Which means we can choose 5 person from the start. Then we select another one from the leftover 4. At last we select the last person from the leftover 3.
Which means we can choose 5 person from the start. Then we select another one from the leftover 4. At last we select the last person from the leftover 3.
Combination
Definition: A way of selecting several things out of a larger
group, where (unlike permutations) order does not matter.
Formula: nCr = nPr / r!
(n-r)!
Problem
Solving
When A,B,C, D and E are lined up for photo shooting sessions, but there’s
only 3 persons are allowed. But then the position doesn’t matters.
The answer is 60 (nPr ) / 3! (r!) X 2! (n-r)! =
5.
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