May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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5-8 Discrete Mathematical Structures
(3) The first seat of men can be occupied in 3 ways and the last seat in 2 ways. Now 4 persons,
that is, 3 women and 1 man can occupy seat in 4! ways. Hence, the total number of ways
is 3.2.4! = 144.
(4) All members of the same sex are seated in adjacent seats is possible in 2.3!3! = 2 × 6 × 6
= 72 ways.
The factor 2 arises due to the fact that in one case men occupy first three seats and then
women and another one in which women occupy first three seats then men.
(5) Men and women are seated alternately in 2(3!)
2
= 72.
Example 7 A state flag is to be designed with 6 vertical strips red, blue, white, ...
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