Question

find the answer of the question

Answer 1

Please see the attachment

Answer 2

Permutation and Combination

There are five countries, in which 5 Indians are there,  4 Bangladeshi, 4 Pakistani, 3 Sri Lankans, 3 Nepalese.

Total number of peoples of different nationality is $(5+4+4+3+3)=19$

For n people to be seated in circular manner, the total arrangements will be (n-1)!, where n is the number of people.

The number of ways in which they can be seated is $19!$ or which can be written as $(n-1)!$ $=(19-1)!=18!$

Hence 19 people can sit around round table is 18!.

If delegates from all nation, have to sit together then the ways in which they can sit is calculate by clubbing the people of same nation and suppose it as one. Like we can club all Indian, Pakistani, Bangladeshi, Sri Lanka, Nepalese as $4 \ people$. So the ways is $(4-1)!=3!$

Again, arranging these nationality people by arranging people among same nationality  .

$=(4-1)!\times5!\times4!\times4!\times3!\times3!=5!\times(4!)^2\times(3!)^3$

Hence, the ways is $5!\times(4!)^2\times(3!)^3$.