Question

16 people, 8 chairs on each side of the table . Four men sit on one particular side and two on other side. Number of ways can they be seated?

a)" "(8!8!10!)/(2!4!)

b)" "(8!8!10!)/(4!6!)

c)" "(8!8!10!)/(2!6!)

a)" "(8!8!10!)/(2!4!6!)

Solution

In the given figure we can see that there are 16 people and 8 chairs are arranged on each side of the table.

Since 4 men sit on one particular side, hence number of ways they can be seated = (8c_4)xx4!

2 men sit on other side of the table, hence number of ways they can be seated = (8c_2)xx2!

Rest other can seat 10! ways.

Now total number of ways 16 men can be seated = ((8c_4)xx4!)xx((8c_2)xx2!)xx10!

= (8!4!)/(4!4!)xx(8!2!)/(2!6!)xx10!

= (8!)/(4!)xx(8!)/(6!)xx10!

= (8!8!10!)/(4!6!)