This document discusses permutations and combinations in discrete mathematics. It defines permutations as arrangements of objects that consider order, and combinations as selections of objects where order does not matter. The fundamental counting principle states that if one event has m outcomes and another n outcomes, the total outcomes of both is m x n. Permutations use factorials and combinations use factorials and binomial coefficients to calculate the number of arrangements and selections. The document provides examples of permutations, combinations, and distinguishes between them.

1. PERMUTATIONS AND COMBINATIONS
•NAME- AURGHYA SAHA
•STUDENT CODE: BWU/BTA/21/109
•Subject : DISCRETE MATHEMATICS
•Course Code : PCC-CSM405

2. OBJECTIVES
 apply fundamental counting principle
 compute permutations
 compute combinations
 distinguish permutations vs combinations

3. OVERVIEW
The study of permutations and combinations is concerned with
determining the number of different ways of arranging and selecting
objects out of a given number of objects without actually listing them.
There are some basic counting techniques which will be useful in
determining the number of different ways of arranging or selecting
objects.

4. FUNDAMENTAL COUNTING PRINCIPLE
 The rule for finding the number of possible outcomes.
States that if an event has “m” possible outcomes and another
independent even has“n” possible outcomes, then there are Mn (m times n)
possible outcomes of the two events together.

5. FUNDAMENTAL COUNTING
PRINCIPLE
Lets start with a simple example.
A student is to flip a coin 6 times. How
many possible outcomes will there be?
1H 2H 3H 4H 5H 6H
1T 2T 3T 4T 5T 6T
6 times*2 possibilities = 12 outcomes
12 outcomes

6. FUNDAMENTAL COUNTING
PRINCIPLE
SHIRTS PANTS SHOES
Red Jeans Tennis
White Khakis Brown
Black Flipflop
3 2 3
x x
How many possible outfits can you make from
the clothing items listed below?
There are 18 outfit
combinations
possible.
= 18

7. PERMUTATIONS
 A permutation is an arrangement of object in a define object
To find the number of Permutations of n items, we can use the
Fundamental Counting Principle or factorial notation. To find the number
of ordered arrangements or Permutations of ‘n’ total items chosen ‘r’ at a
time. The notation for the number of r-permutations: P(n,r).
you can use the formula:
where 0  r  n
.
n!
(n 
r)!
n p 
r

8. COMBINATIONS
On many occasions we are not interested in arranging but
only in selecting r objects from given n objects. A
combination is a selection of some or all of a number of
different objects where the order of selection is
immaterial. The number of selections of r objects from
the given n objects is denoted by nCr ,and is given by
nCr =n!/ r! (n-r)!

9. DISTINGUISH PERMUTATIONS
VS
COMBINATIONS
PERMUTATIONS
Arranging people,
digits, numbers,
alphabets, letters,
colours.
Keywords:
Arrangements,
arrange,…
COMBINATIONS
Selection of menu,
food,
clothes, subjects,
teams.
Keywords: Select,
choice,…

10. DISTINGUISH PERMUTATIONS
VS
COMBINATIONS

11. Thank You