Delegates from 24 countries participate in
a round table discussion. Find the number
of seating arrangments where two specified
delegates are. (a) always together, (b) never
together.
Answers
Answered by
1
Given:
Total number of delegates = 24
To Find:
Seating arrangement when they are always together
Seating arrangement when they are never together
Solution:
Always together -
Let two delegates be = 1 unit
Thus, they can be arranged in ways = 2!
The two delegates are to be seated with other 22.
Thus, total number of ways when they are always together
= 22! x 2!
Never together-
When two are never together, then 22 will participate in ways = 21!
Therefore, there will be 22 places of which any two places will be filled by two who are never together.
Thus, two specified will be arranged in = 22P2
= 22P2 x 21!
= 22!/( 22 - 2)! x 21!
= 22!/20! x 21!
= 21 x 22 x 21!
= 21 x 22!
Answer: Always together - 22! x 2!, never together - 21 X 22!
Similar questions