请问 GWD Math 28-37怎么解？

wyf007

Q37:
In a meeting of 3 representatives from each of 6 different companies, each person shook hands with every person not from his or her own company.  If the representatives did not shake hands with people from their own company, how many handshakes took place?

A.    45
B.    135
C.    144
D.    270
E.    288

wyf007

是不是一下解法？
Answer: C(1,3)*C(1,15)+C(1,3)*C(1,12)+C(1,3)*C(1,9)+C(1,3)*C(1,6)+C(1,3)*C(1,3)

sue101

C(2,18）-6C(2,3)=135