Question

find number of ways of arranging Chief Minister and 10 cabinet ministers at a circular table so that the Chief minister always sits in a particular seat

Answer 1

There is 11 seat on the roundtable.
One seat particular selected for Chief minister then there are remaining 10 seats for 10 cabinet minister.
Then
1 person can be seated at a table (with one chair) one way. (1 x 1)

2 people can be seated at a table (with two chairs) two different ways. (2 x 1)

3 people can be seated at a table (with three chairs) six different ways. I will list them: abc, acb, bac, bca, cab, and cba. (3 x 2 x 1)

4 people can be seated at a table (with four chairs) 24 different ways. (abcd, abdc, acbd, acdb, adbc, adcb, bacd, badc, bcad, bcda, bdac, bdca, etc.)

10 people can be seated at a table (with ten chairs except for cheif minister chair) :10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
=10! = 3,628,800 Ans.