ii)Permutation
Definition :
arrangement that can be made by taking some or all of a number of things,
Formula :nP ͬ
= n!/(n-r)!
n,r : non negative integers (r <= n)
r : size of the each permutation
n : size of set from which elementsare permuted
! : factorial operator
Question
:
If you have 6 new year greeting cards and you
want send them to 4 of your friends, in how many ways can this be done?
Solution :
We have to find number of permutation of 4
objects out of 6 objects. This number is 6P4 = 6(6-1)(6-2)(6-3) = 6*5*4*3 = 360
Therefore, cards can be sent in 360 ways
6P4 = 6! / (6-4)!
iii)Combination
Definition :
A
combination is a selection of some or allof a numberof different object. It is
an un-ordered collection of unique sizes,
Formula : nC ͬ
= nP ͬ /r!
n,r : non negative integers (r <= n)
r : size of the each permutation
n : size of set from which elementsare permuted
! : factorial operator
Question
:
In a box, there are 5 black pens, 3 white pens
and 4 red pens. In how many ways can 2 black pens, 2 white pens and2 red pens
can be chosen?
Solution :
No of ways of choosing 2 black pens from 5
black pens
5C2=5P2/2!=5*4/1*2=10
No of ways of choosing 2 white pens from 3
white pens
3C2=3P2/2!=3*2/1*2=3
No of ways of choosing 2 red pens from 4 red
pens
4C2=4P2/2!=4*1/1*2=6
Therefore, it can be chosen by 10*3*6=180 ways
hy
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