Wednesday, 22 May 2013

Task 7

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.
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.

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.











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.


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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