Slide 1 : Prepared By Shijna
Permutations & Combinations : Permutations & Combinations
Slide 3 : Permutations
In how many ways you can wear these shirt and pants? : In how many ways you can wear these shirt and pants?
Slide 5 :
Combination of flavors in Ice cream : Combination of flavors in Ice cream
To open a number lock the position of numbers is Important : To open a number lock the position of numbers is Important
Permutation – Position : Permutation – Position A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.
Arrangement --- : Arrangement --- ROSE, NUMBER, etc
Formula Factorial notation : Formula Factorial notation nPr= n!
nPr=n!/(n-r)! , 0 = r = n
Theorem 2: The number of permutations of n different objects taken r at a time,where repetition is allowed, is nPr. : Theorem 2: The number of permutations of n different objects taken r at a time,where repetition is allowed, is nPr.
Permutations when all the objects are not distinct objects. : Permutations when all the objects are not distinct objects.
Slide 13 : Theorem 3
The number of permutations of n objects, where p objects are of the
same kind and rest are all different =
!
!n
p
Slide 14 : Theorem 4
The number of permutations of n objects, where p1 objects are of one kind, p2 are of second kind, ..., pk are of kth kind and the rest, if any, are of different
kind is
1 2
!
! ! k!
n
p p ...p
s : s