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
Total number of representatives = (number of representatives per company)(total number of companies) = 3*6 = 18.
Good handshakes = total possible handshakes - bad handshakes.
Total possible handshakes:
From the 18 representatives, the total number of pairs that could shake hands = 18C2 = (18*17)/(2*1) = 153.
Bad handshakes:
A bad handshake occurs when a pair of representatives from the same company shake hands.
From each group of 3 representatives from the same company, the total number of pairs that could shake hands = 3C2 = (3*2)/(2*1) = 3.
Since there are 6 companies -- and each company yields a total of 3 bad handshakes -- the total number of bad handshakes = 6*3 = 18.
Good handshakes:
(total possible handshakes) - (bad handshakes) = 153 - 18 = 135.
The correct answer is
B.
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