Question

In how many ways 4 Indian and 4 Pakistani army Generals can be seated, half on each side of a long table, so that no two Indian Generals may be together?

(i) Find the number of sitting arrangements.

(ii) Do you feel that periodic meeting between senior officers and politicians are in the interest of both the countries for keeping peace and goodwill in the region? Express your views briefly.

Answer 1

On the first side of a long table, two Indians and two Pakistani army Generals can be selected in ${}^4{C}_2{\times }^4{C}_2$ ways. Firstly, we fix the Ist and IIIrd positions of Indian army and IInd and IVth positions of Pakistani army, they can be seated in 2! $\times 2!$, but they can interchange their position in 2 ways. Thus, in first side of a table, the number of ways of sitting army Generals.

=${}^4{C}_2{\times }^4{C}_2\times 2\times 2!\times 2!=6\times 6\times 2\times 2\times 2=288$[1]

Similarly, remaining two Indian army and two Pakistani army can be seated in ${}^2{C}_2{\times }^2{C}_2\times 2\times 2!\times 2!=1\times 1\times 2\times 2\times 2=8$

(i) The total number of sitting arrangements = $288\times 8=2304$

(ii) Yes; by the frequent meeting and goodwill missions, misunderstanding between two countries will reduce drastically.