The document discusses permutations and combinations. It defines a permutation as an arrangement of objects where order matters, and a combination as an arrangement where order does not matter. It provides examples of permutations of sets with 3 and 8 elements. The number of permutations of a set of n elements is n factorial. Permutations are arrangements of all elements of a set. The document also provides examples of calculating the number of permutations in different scenarios like seating arrangements and rearrangements of letters in a word.
4. If the order doesn't matter, it is a Combination.
If the order does matter it is a Permutation.
there are six permutations of the set:
{1,2,3},
(1,2,3), (1,3,2), (2,1,3),
(2,3,1), (3,1,2), (3,2,1).
5. The number of permutations of n distinct
objects is n factorial usually written as
“n! “, which means the product of all
positive integers less than or equal to
”n”.
6.
7. A permutation of a set S is defined as
a bijection from S to itself. The collection
of such permutations form a symmetric
group. Permutations may act on
structured objects by rearranging their
components, or by certain replacements
(substitutions) of symbols.
8. the r-permutations, or partial
permutations, are the ordered
arrangements of r distinct elements
selected from a set. When r is equal to
the size of the set, these are the
permutations of the set.
9. Example 1:
n! = n(n-1)(n-2)…1
9! = 9*8*7*6*5*4*3*2*1
answer = 362,880
By definition:
1! = 1 and 0! = 1
Formula:
n!
10. How many ways can 8 students be seated in a row of 6
chairs?
Solve by (a) Multiplication rule & (b) Permutation of
n things taken r at time.
FORMULA:
nPr = n!
(n-r)!
11. Notation:
Example 2:
Given:
n = 8, r = 6
Solution:
= 8! = 8! = 40320 = 20,160
(8 – 6)! 2! 2
or
Manual = 8*7*6*5*4*3*2! ÷ 2!
= 20,160
Formula:
nPr = n!
(n – r)!
12. How many ways can 8 people sit around a round table?
FORMULA:
(n-1)!