Answer: B. 135
Step-by-step explanation:
Given : Number of representatives from each company = 3
Number of companies =6
Total number of people there : [tex]6\times3=18[/tex]
The total number of ways that 18 people shake hands with each other :-
[tex]^{18}C_{2}=\dfrac{18!}{2!(18-2)!}=\dfrac{18!}{2(16!)}=153[/tex]
The number of ways that representatives shake hands with people from their own company :-
[tex]6\times^3C_2=6\times3=18[/tex]
If the representatives did not shake hands with people from their own company , then the total number of ways for handshake :-
[tex]153-18=135[/tex]
Hence, the total number of handshakes will be 135.
