Question

in how many ways could king authur and six of his court sit at the round table when one of the chairs was the throne chair for king arthur and there were six other chairs?

Answer 1

King Arthur will sit at his throne, rest six chairs will be occupied by his court
6 persons on 6 chairs
First chair can be occupied by 6 persons
second can be occupied by 5 persons
so no. of ways
\[6\times 5\times 4......\times 1=6!\]

Answer 2

do you understand ?

Answer 3

oh thank you wait can you help me on this one?

At the head table at a banquet are seated two senators, two governors, and three mayors. Find the number of ways in which these seven people can be seated under the conditions described: A mayor is at each end and the senators are in consecutive seats

Answer 4

just a moment

Answer 5

Table will be like this
Small squares represent chairs