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Permutations And Combinations (view source)
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= Permutations & Combinations =
== Fundamental Counting Principle ==
== Fundamental Counting Principle ==
If an activity can be done in ‘m’ ways and other activity can be done in ‘n’ ways, the total number of ways of doing the activity one after the other is '''m X n'''
If an activity can be done in ‘m’ ways and other activity can be done in ‘n’ ways, the total number of ways of doing the activity one after the other is '''m X n'''
to draw the second, so there are a total of 52*51 = 2652 ways to draw
to draw the second, so there are a total of 52*51 = 2652 ways to draw
the two cards.
the two cards.
== Permutations ==
A permutation is one of the different arrangements of a group of items where order matters.
Consider the following:
Given 3 people, Brinda, Mary and Shariff, how many different ways can these three people be arranged where order
matters?
Let BMS stand for the order of Brinda on the left, Mary in the middle and Shariff on the right.
Since order matters, a different arrangement is BSM. Where Brinda is on the left, Shariff is in the middle and Mary is on the right.
If we find all possible arrangements of Brinda, Mary and Shariff where order matters, we have the following:
BMS, BSM, MSB, MBS, SMB, SBM
The number of ways to arrange three people three
at a time is: ''' 3! = (3)(2)(1) = 6''' ways
There are n! ways to arrange n
objects in groups of n at a time.
The number of permutations of n objects taken r at
a time is:
[[Image:KOER%20Probability,%20Permutations%20and%20Combinations_html_5d806af0.gif]],
this is when there are <u>no repetitions</u>.
== Combinations ==
A combination is of a grouping of items where order does not matter. Example creating subgroups of 3 from Sub groups of 3 from a team of fifteen.
Consider the following:
Given 3 people, Brinda, Mary and Shariff, how many different ways can these three people be selected to form a group?
Since order does not matter, any arrangement with Brinda, Mary and Shariff is considered the same .
Therefore the only one way of grouping 3 people.
Now suppose we want to take four people, Brinda, Mary, Shariff and Anita, and arrange them in groups of three at a
time where order does not matter. The following demonstrates all the possible arrangements.
BMS, MSA, BMA, BSA
There are 4 ways to group 4 people in groups of 3 at a time.
The number of combinations of a group of n objects taken r at a time is:
when no repetitions are allowed.
= Textbook =
= Textbook =
