Question

At a meeting of 3 representatives from each of 6 different companies, each person shook hands once 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. 45B. 135C. 144D. 270E. 288

Answer 1

Answer: B. 135

Explanation:

Given : Number of representatives from each company = 3

Number of companies =6

Total number of people there :
`6*3=18`

The total number of ways that 18 people shake hands with each other :-

`^(18)C_(2)=(18!)/(2!(18-2)!)=(18!)/(2(16!))=153`

The number of ways that representatives shake hands with people from their own company :-

`6*^3C_2=6*3=18`

If the representatives did not shake hands with people from their own company , then the total number of ways for handshake :-

`153-18=135`

Hence, the total number of handshakes will be 135.