Page 171 - DMTH202_BASIC_MATHEMATICS_II

Basic Mathematics-II

Notes hexagons must be grouped together. In how many different ways can each type of object be
arranged?
The group of 3 distinguishable squares can be arranged in 3! ways, the 4 distinguishable triangles
in 4! ways, and the 7 distinguishable hexagons in 7! ways. Given that we have 3 groups of
distinguishable objects, we can arrange those groups in 3! ways. Thus, the number of
distinguishable arrangements of the objects when they must be grouped by type is
3!  4!  7!  3! = 4,354,560

Task A coach must select five starters from a team of 12 players. How many different
ways can the coach choose the starters?
Self Assessment

Fill in the blanks:
8. A ...................................., also recognized as an “arrangement number” or “order,” is a
reorganization of the essentials of an ordered list into a one-to-one
correspondence with itself.
9. A permutation of ordered objects in which no object is in its ordinary place is known as
..................................... .
10. The permutations of a list can be instituted in Mathematica by means of the command
..................................... .

11. Permutations are normally indicated in ..................................... order.
12. A demonstration of a permutation as a product of permutation cycles is ............................. .

12.4 Circular Permutation

Circular-permutations consists of two phases:
(a) If clockwise and anti-clock-wise orders are dissimilar, then total number of circular-
permutations is specified by (n–1)!
(b) 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!
Proof (a):

(a) Le us suppose that 4 persons A,B,C, and D are sitting about a round table

166 LOVELY PROFESSIONAL UNIVERSITY