Page 174 - DMTH202_BASIC_MATHEMATICS_II

Unit 12: Permutation

 A permutation, also recognized as an “arrangement number” or “order,” is a reorganization Notes
of the essentials of an ordered list S into a one-to-one correspondence with S itself.

 A permutation of ordered objects in which no object is in its ordinary place is known as
derangement (or at times, a complete permutation) and the number of such permutations
is specified by the sub factorial ! n.

 A permutation of n objects taken r at a time is a selection of r objects from a total of n

objects (r  n), where order matters.
 The permutations of a list can be instituted in Mathematica by means of the command
Permutations.
 If clockwise and anti clock-wise orders are dissimilar, then total number of circular
permutations is specified by (n – 1)!
 ?If clock-wise and anti-clock-wise orders are considered as not dissimilar, then total number
of circular-permutations is specified by (n – 1)!/2!

12.6 Keywords

Factorial: It determines the number of different ORDERS in which one can arrange or place set
of items such as n!= n x (n–1) x (n–2) x (n–3)...3 x 2 x 1.

Permutation: A permutation of n objects taken r at a time is a selection of r objects from a total
of n objects (r  n), where order matters.

12.7 Review Questions

1. In a race with 10 horses, the first, second, and third place finishers are noted. How many
outcomes are there?
2. Eight persons, consisting of four married couples, are to be seated in a row of eight chairs.
How many seating arrangements are there if:

(a) There are no other restrictions
(b) The men must sit together and the women must sit together
(c) The men must sit together
(d) The spouses in each married couple must sit together
3. Suppose that n people are to be seated at a round table. Show that there are (n – 1)! distinct
seating arrangements.
4. How many different ways can 3 red, 4 yellow and 2 blue bulbs be arranged in a string of
Christmas tree lights with 9 sockets?
5. How many numbers greater than 1000 can be formed with the digits 3, 4, 6, 8, 9 if a digit
cannot occur more than once in a number?
6. Expand the factorial (n + 2)! / n!
7. Evaluate (n - 1)! / (n + 1)!
8. How many permutations of 3 different digits are there, chosen from the ten digits 0 to 9
inclusive?
9. In how many ways can a committee of 5 be chosen from 10 people?

LOVELY PROFESSIONAL UNIVERSITY 169