Question

Delegates from 24 countries participate in a round table discussion. Find the number of seating arrangements where two specified delegates are never together.

Answer 1

When 2 specified delegates are never together then, the other 22 delegates can participate in a round table discussion in (22  1)! = 21! ways.
∴ There are 22 places of which any 2 places can be filled by those 2 delegates who are never together.
∴ Two specified delegates can be arranged in ²²P₂ ways.
∴ Total number of arrangements if two specified delegates are never together
= `""^22"P"_2xx21!`

= `(22!)/((22-2)!)xx21!`

= `(22!)/(20!)xx21!`
= 22 × 21 × 21!
= 21 × 22 × 21!
 = 21 × 22!