In general there are two fundamental principle of counting. These are addition principle and multiplication principle.
The rule of sum: If a first task can be performed in m ways, while a second task can be performed in n ways, and the tasks cannot be performed simultaneously, then performing either task can be accomplished in any one of m+n ways.
The boss assigns 12 employees to two committees.
- Committee A consists of five members.
- Committee B consists of seven members.
- If the boss speak to just one member before making a decision, …?
- If he speak to one member of committee A on the first day, and another member of committee B on the second day, …?
If a procedure can be broken down into first and second stages, and if there are m possible outcomes for the first stage and if, for each of these outcomes, there are n possible outcomes for the second stage, then the total procedure can be carried out, in the designated order, in mn ways.
A license plate consists of two letters followed by four digits.
- If no letter or digit can be repeated?
- If repetitions of letters and digits are allowed?
- If repetitions of letters and digits are allowed, how many of the plates have only vowels (A, E, I, O, U) and even digits?
- n factorial is defined by (a) 0!=1; n!=n(n-1)(n-2)…(2)(1)
- Given a collection of n distinct objects, any (linear) arrangement of these objects is called a permutation of the collection
The number of permutations of size r from a collection of n distinct objects is P(n, r)=n!/(n-r)!.
Addition Principle:
Fundamental principle of counting in an event can occur in m different way and another event can occur in n different ways then either of the two events can occur in (m+n) ways provided only one event can occur at a time.
Multiplication principle:
Fundamental principle of counting in an event can occur in m different ways and if corresponding to each way of occurring there are n different ways of the second operation then both the operations can occur simultaneousely in (mn) ways.
Example of Multiplication Principle and Factorial Notation:
For example consider a cinema hall with 4 entrance and 5 exits. Therefore , the number of ways that a person can enter and exit from the cinema hall is (4x5) = 20. Similarly, the number of ways that a person can either enter or out from the cinema hall is (4+5) = 9.
The rule of sum: If a first task can be performed in m ways, while a second task can be performed in n ways, and the tasks cannot be performed simultaneously, then performing either task can be accomplished in any one of m+n ways.
The boss assigns 12 employees to two committees.
- Committee A consists of five members.
- Committee B consists of seven members.
- If the boss speak to just one member before making a decision, …?
- If he speak to one member of committee A on the first day, and another member of committee B on the second day, …?
If a procedure can be broken down into first and second stages, and if there are m possible outcomes for the first stage and if, for each of these outcomes, there are n possible outcomes for the second stage, then the total procedure can be carried out, in the designated order, in mn ways.
A license plate consists of two letters followed by four digits.
- If no letter or digit can be repeated?
- If repetitions of letters and digits are allowed?
- If repetitions of letters and digits are allowed, how many of the plates have only vowels (A, E, I, O, U) and even digits?
- n factorial is defined by (a) 0!=1; n!=n(n-1)(n-2)…(2)(1)
- Given a collection of n distinct objects, any (linear) arrangement of these objects is called a permutation of the collection
The number of permutations of size r from a collection of n distinct objects is P(n, r)=n!/(n-r)!.
Addition Principle:
Fundamental principle of counting in an event can occur in m different way and another event can occur in n different ways then either of the two events can occur in (m+n) ways provided only one event can occur at a time.
Multiplication principle:
Fundamental principle of counting in an event can occur in m different ways and if corresponding to each way of occurring there are n different ways of the second operation then both the operations can occur simultaneousely in (mn) ways.
Example of Multiplication Principle and Factorial Notation:
For example consider a cinema hall with 4 entrance and 5 exits. Therefore , the number of ways that a person can enter and exit from the cinema hall is (4x5) = 20. Similarly, the number of ways that a person can either enter or out from the cinema hall is (4+5) = 9.
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