a presantation on permutation and combination

1. Amna nazir 59
Syeda shajiah zahra zaidi 14
Muazma nageen 06
Muqadas fatima 22
Adeera wasiq 20

3. Permutation
 Definitons:
The number of permutation of ‘n’ objects taken ‘r’ at a
time is the quotient of n! and (n-r)!
 Formula :
nPr= __n!__
(n-r)!

4. permutation
 An arrangement or listing in which order or placement
is important is called a permutation.
 Simple example “combination lock”.
 31-17-5 and 5-17-31 are not same .
 Thus order is very important.

5. example of permutation
Q: A computer programmer is using 7 digit
registration code made up of 1,2,4,5,6,7and 9 each
number has to be used and no number should be
repeated

6. Solution
 By using permutation formula
 7P7 = __7 !__
( 7-7)!
=7*6*5*4*3*2*1
1
=5040

7. combination
 Definition:
The number of combinations of ‘n’ object taken ‘r’ at a
time is the quotient of n! and (n-r)!*r!
 Formula :
nCr = ____n!___
(n-r)!*r!

8. combination
 An arrangement or listing in which order is not
important is called combination.
 For example if you are choosing two objects from the
list of ten then the order in which you choose the
objects does not matters.

9. example of combination
Q :The student of Mr.fants seminar class had to choose 4
out of 7 of the people who were nominated to serve on
the student council how many different groups of
people can be selected?

10. Solution
 By using formula of the combination
 nCr = 7C4
=___7!__
(7-4)!*4!
= 7*6*5*4*3*2*1
(3)!*4*3*2*1
=7*6*5
3*2*1
=35

11. Real numbers
 Real numbers are the numbers that consist of all
rational irrational numbers.
 The real number system has many subsets such as
 Natural number
 Whole number
 Integer

13.  Terminating decimal number are number with finite
digits
 Non terminating number are the decimal number with
infinite digits
 Repating decimal number are the number with
repeating infinite digits
 Non repeating decimal number are the number with
non repeating infinite digits

14. Rational number
 Rational numbers are the numbers that can be
expressed in the form of a/b where a and b are integer
and b=0
 They can always be expressed using terminating
decimal or repeating decimal
 Example: 2/3,6/7

15. Natural numbers
 Natural numbers are the set of counting numbers
which starts from 1.
 They are denoted by N
 Example:
 {1,2,3,4,5,6,7………………}

16. Whole number
 Whole numbers are the set of numbers that include 0
plus the set of natural number
 Example:
 {0,1,2,3,4,5,6………}

17. Integer
 An integer is a whole number(not a factorial number)
that can be positive ,negative and zero.
 It is denoted by Z.
 Z={…..-2,-1,0,1,2…..}

18. Irrational number
 Irrational number are any number that can not be
expressed as a/b
 They are expressed as non terminating ,non repeating
decimal (decimal that go on forever)
 Example:
 3.8767525634658236……
 Pie ( )