Fifteen persons sit around a table. Find the number of arrangments that have two specified persons not sitting side by side.

A committee of 10 members sits around a table. Find the number of arrangements that have the president and the vice president together.

Five men, two women, and a child sit around a table. Find the number of arrangements where the child is seated (a) between the two women (b) between two men

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.

A party has 20 participants. Find the number of distinct ways for the host to sit with them around a circular table. How many these ways have two specified persons on either side of the host?

Eight men and six women sit around a table. How many of sitting arrangements will have no two women together?