Since all the 4 teachers sit together, group them together and consider as a single teachers. Hence, n = total number of persons-12+1=13 These 13 persons can be seated at a round table in (13-1)! =12! ways... (A) However these 4 teachers can be arranged

Let Fix one student at the circular Table then remains students: (10-1)! Total way to arrange 10 Teachers:10! Total way to arrange students and teachers according to condition: 9!*10*

Using formula C(n,2)= n(n-1)/2 Total no. Of handshake =10 n(n-1)/2 = 20 n(n-1)=40 n = 4

Using formula C(n,2)= n(n-1)/2 Total no. Of handshake =6 n(n-1)/2 = 6 n(n-1)=12 n = 4 [4*3=12]